In 1902, the caustic American satirist Ambrose Bierce – who once reviewed a book by observing that its covers were "too far apart" – proposed a new social convention. Modern life, he complained, involved being introduced to far too many people: you'd meet a friend in the street, then a friend of his would stroll by, and before you knew it you'd have a new, unasked-for acquaintance, with all the obligations that entailed. Bierce blamed the democratic spirit of the 20th century: in the older, more formal days, stricter rules governed who could form acquaintanceships with whom. "It is to be wished," Bierce wrote, "that some great social force, say a billionaire, would set up a system of disintroductions." He imagined a generous gent, a Mr White, resolving to disintroduce two friends of his, Mr Black and Mr Green. "Mr Black," he might say, "knowing the low esteem in which you hold each other, I have the honour to disintroduce you from Mr Green." Mr Black (bowing): "Sir, I have long desired your unacquaintance." Mr Green: "Charmed to unmeet you, sir." Mr White: "I'm sure you will become very good strangers."

It's probably best, for Bierce's sake, that he never lived to see Facebook's People You May Know. Ever since the widespread adoption of email in the 1990s, in fact, the phenomenon he bemoaned has reached a scale he could never have imagined. Technology exposes us to vastly more opportunities for making social connections, and far more effortlessly than even a stroll down the street and a handshake. Yet an etiquette for terminating those links, should they outlive their mutual benefit – if they ever had any – remains as absent as ever. Even "unfriending" someone on Facebook, the closest equivalent to Bierce's proposal, feels like delivering a slap in the face (and not even a well-timed slap, since you can't be sure when they'll find out). Facebook itself hates unfriending, for commercial reasons, and thus makes it easy to hide updates from tiresome contacts without their knowing – a deeply unsatisfactory arrangement that leaves you at constant risk of meeting someone face-to-face who assumes you must already know they've got engaged, or had another baby, or been dumped, or fired, or widowed.

The result – at least for anyone who can still recall friendship before the social media age – can be an awkward hodgepodge. There are Facebook friends with whom you want to share everything, those you've grown apart from, and those you've barely heard of. (You can assign them to different lists, but then you've introduced a whole new layer of decisions: who belongs where? What qualifies someone to be switched from one list to another? And so on.) There are Twitter followers with whom your acquaintance is strictly professional, those you know from school, but didn't necessarily like, and those who are your dad. Not long ago, I realised, with a feeling of dismay, that I'd started to think of some of these contacts – not most of them, but some – as clutter.

If that sounds a heartless way to think about other people, consider the parallels. Physical clutter, as a widespread problem, is only as old as modern consumerism: before the availability of cheap gadgets, clothes and self-assembly furniture, it wasn't an option for most people to accumulate basements full of unwanted exercise bikes, games consoles or broken Ikea bookshelves. We think we want this stuff, but, once it becomes clutter, it exerts a subtle psychological tug. It weighs us down. The notion of purging it begins to strike as us appealing, and dumping all the crap into bin bags feels like a liberation. "Friend clutter", likewise, accumulates because it's effortless to accumulate it: before the internet, the only bonds you'd retain were the ones you actively cultivated, by travel or letter-writing or phone calls, or those with the handful of people you saw every day. Friend clutter exerts a similar psychological pull. The difference, as Bierce understood, comes with the decluttering part: exercise bikes and PlayStations don't get offended when you get rid of them. People do. So we let the clutter accumulate.

Or most of us do. Last year, a writer of romance novels from Illinois named ArLynn Presser embarked upon what you might call an audit of her so-called friends – the social equivalent of picking up each old gadget and scrutinising it, before keeping it or throwing it out. She was recently divorced, and her adult children had left home – "If your kids don't call you a lot, that's a sign you've done a good job," she told me – and she was spending hours every day on Facebook. "I was keeping up with everybody's news, noticing what they were doing, staying up to date, and I began to think, 'Seriously though, who are these people? If I was in college with you, and we weren't particularly good friends then – why are you suddenly someone I message back and forth with at least once a day?'" Politeness, she knew, was the reason she'd accepted some of her online friends: "Say someone sends a request and you look at your mutual friends and you wonder, 'Wait – were you the person I was talking to at that wedding?' You don't want to ask, 'How, exactly, do I know you, and why would I want to be your friend?'" Presser had 325 Facebook friends, a little money stashed away, and a fear of flying that she wanted to overcome, so she decided to combine all three: she made a New Year's resolution to visit them all, to find out why – or, indeed, whether – they were friends.

"I don't think I realised," Presser says, "that it was going to be quite as big a deal as it was."

To recognise that friend clutter is a problem, it should be emphasised, doesn't mean condemning online friendship per se. It's commonplace, these days, to encounter the concern that social media might be making us lonelier – that online bonds can't be as fulfilling as "real-life" ones. The sociologist Sherry Turkle, author of the recent book Alone Together, worries that "we have sacrificed conversation for mere connection. Email, Twitter, Facebook, all of these have their places… but no matter how valuable, they do not substitute for conversation." One frequently cited statistic, based on research among Americans, is that between 1985 and 2004 the number of people who said they didn't have a single "confidant" – someone to whom they could talk about anything – rose from 10% to 25%. A further 20% had only one such person. It might seem hard to avoid the conclusion that all the time we spend online, superficially connected but in a more profound sense isolated, must be to blame.

Except that, according to an ever-growing body of evidence, social media isn't making us lonelier or less deeply connected. Instead, study after study endorses the idea of "media multiplexity": people who communicate lots via one medium, it turns out, are the kind of people who communicate lots via others as well. Regular emailers are more likely also to be regular telephoners, one study found; people who use Facebook multiple times a day, according to another investigation, have 9% more close ties in their overall social network, on average, than those who don't. Social media builds social capital, rather than degrading it: regular users of Facebook, LinkedIn and Twitter, one major survey last year concluded, are 43% more likely to vote. Even that chilling statistic about more Americans lacking a confidant now looks dubious: a new analysis by the sociologist Claude Fischer concluded that the finding arose because of a change in how the questions were asked. There's little other evidence to suggest that more people are feeling lonelier. Which makes it tricky to maintain that the new modes of friendship are eroding friendship itself.

None of this means that friendship isn't being transformed by social media, though. It's just that the problems aren't those of isolation – of the replacement of face‑to‑face contact with screen-gazing in darkened rooms – but those of scale. The anthropologist and evolutionary psychologist Robin Dunbar famously calculated "Dunbar's number" – the notion that the largest number of meaningful social relationships that any one person can maintain is somewhere around 150. Before the internet, we kept things manageable by natural attrition: if there were people you didn't want to see any more, then by and large you didn't see them. "It's unnatural for us to drag all our past relationships with us into our future, as we do with Facebook," says Anjali Mullany, social media editor of Fast Company and writer of its "social media agony aunt" column. "That's not how things have worked, in terms of friendship, for thousands of years."

Online networks have a tendency to obliterate the nuances between different kinds of relationships. Despite Facebook's lists, privacy settings and the rest, Mullany points out, "ultimately, somebody is either your friend on Facebook or they're not. In real life, we're very political about our friendships, and I don't mean that in a bad way." There are friendships we'll let fade to nothing; others for which we'll put on a facade for a few hours at Christmas; or friendships of necessity, where we'll give the impression of intimacy without the reality. In contrast, "Facebook essentially doesn't allow us to be political." Its founder, Mark Zuckerberg, makes no secret of his belief that everybody sharing everything with everybody else would be Facebook's ideal state. (The site's more nuanced levels of user control are provided, his statements imply, only as a grudging concession to old‑fashioned attitudes that will soon die out.) It's no coincidence, of course, that maximal sharing means maximally lucrative opportunities for advertising. But this flattening of relationships is unlike anything we've called "friendship" before.

When Presser set out to meet her Facebook friends, one of the first things she discovered was that about two dozen of them had no intention of letting her visit, which certainly answered the question of what kind of friends they were. More revelations were in store. Some people proved overly demanding, such as the woman with whom she'd grown up and who had moved to a remote part of Turkey – she said Presser could visit so long as she brought her a Mac computer and a printer. When Presser offered to help her have the equipment shipped instead, she says, she found herself unfriended. Then there was the childhood acquaintance with whom, Presser realised, she'd stayed Facebook friends mainly to avoid giving the impression that she had a problem with his having undergone gender reassignment surgery to become a woman. But when they met, they still didn't get along: "I didn't like her any more than I had done as a child." Another Facebook friend, whom she visited in Boston, seemed friendly enough: they went to a yoga class together and said warm goodbyes at the airport. Waiting for her flight, Presser blogged about the yoga class in a slightly facetious manner. "By the time I got off the plane," she recalls, "I'd been defriended and blocked."

Presser is at pains to point out that her expedition, which she plans to use as the basis for a book, was a largely positive experience. In a remote corner of Alaska, she rekindled an old friendship; near Beachy Head, she was served a splendid Sunday dinner by people she'd never met; again and again, she was moved by the generosity of people "who, after all, hadn't signed up to my resolution". But her year of friend‑auditing was clarifying, too. The realisation that she didn't have much in common with certain Facebook "friends" meant they no longer needed to weigh on her mind; she could focus on the other ones instead.

Not that it would be accurate to give the impression that Presser reduced her number of Facebook friends. Mentally, she had decluttered. But thanks to the publicity her quest attracted in the US media – and her seeming inability to decline new requests – her friend count stands at 5,000. Facebook won't let her add more.

The more profound truth behind friend clutter may be that, as a general rule, we don't handle endings well. "Our culture seems to applaud the spirit, promise and gumption of beginnings," writes the sociologist Sara Lawrence-Lightfoot in her absorbing new book, Exit: The Endings That Set Us Free, whereas "our exits are often ignored or invisible". We celebrate the new – marriages, homes, work projects – but "there is little appreciation or applause when we decide (or it is decided for us) that it's time to move on". We need "a language for leave-taking", Lawrence-Lightfoot argues, and not just for funerals. A terminated friendship, after all, needn't necessarily signal a horrifying defeat, to be expunged from memory. One might just as easily think of it as "completed".

Mullany recommends a friend-decluttering exercise that she admits sounds "weird", but that she predicts will become more and more widely accepted. She advises making a public proclamation on Facebook in which you specify the criteria by which you'll henceforth be defining people as "friends". Maybe you'll resolve only to remain Facebook friends with people you've met at least once in real life, or maybe you'll use a stricter standard, such as whether you'd invite that person to your wedding. Explain, in the same proclamation, that the consequent defriending shouldn't be taken personally, and that you're doing it to a number of people at once. Then start clearing out the clutter. Increasingly, Mullany argues, social media will force us to evaluate our friendships in this way – to take stock of our connections, so as to reserve our energies for those who matter most. She equates this to drawing up the guest list for a wedding: "It's stressful but, for many people, making that list is a really important, meaningful moment."

A person involved in the music industry whom I'll call Andrew – because telling you his real identity would defeat all his efforts to manage his online presence – recalls the moment he realised he'd need two Twitter profiles: one for his public existence and one for his actual friends. (The problem is somewhat different on Twitter, since followers don't need to be approved.) "You forget that there's an audience," he says. "I'd be saying something to a friend, and then someone I didn't know would chip in, furiously angry about what I'd said. I thought, 'I can't be fucking bothered with this.' It was like dragging a busload of people behind you wherever you went." Andrew left Facebook for similar reasons. "Somebody I'd been at school with when I was 10 sent me a message to say, 'Are you still really into Adam And The Ants?' Of course I'm not. I'm in my 40s, and we knew each other when we were 10."

If Zuckerberg's insistence that everyone should be friends with everyone prompts us, out of necessity, to winnow our lists to a smaller group of people we truly cherish, he'll have done something admirable, even if it's the opposite of what he intended.

And what of Bierce, who was longing for a new convention of disintroductions as long ago as 1902? He handled his own exits unconventionally, to say the least. In 1913, at the age of 71, he took off for Mexico, telling friends he wanted to witness the revolution underway there. Some time later, he is supposed to have written, in a letter to a friend, "I leave here tomorrow for an unknown destination", though the letter has never been found. Then he vanished. There were rumours – one involved his execution by a Mexican firing squad – but nothing was ever confirmed. Gradually, it began to dawn on Bierce's friends that, one way or another, he'd disintroduced himself from them all.