Last week I was infuriated by a study. I'm not talking about the type of room – I wasn't maddened by a den or seething at the sight of a home office. I was annoyed by a "survey", a "report", some "research". It was given all sorts of titles in the press, none of which was "pile of sanctimonious crap", which is a shame because that's what it was.

Some people at Netmums, which I'm guessing is the Pepsi to Mumsnet's Coke (irresponsible though it is of me to mention either high-sugar drink when children might be reading), had decided the world might be a better place if they found some way of slagging off The Simpsons. And, while they were at it, The Flintstones and Peppa Pig and The Gruffalo and My Family and Outnumbered. All of those enjoyable entertainments, and My Family, were criticised for their negative depictions of fathers. It was like the RSPCA moaning that Tom and Jerry is an unrepresentative depiction of the behaviour of the domestic cat or the Institute of Hospitality complaining that Fawlty Towers puts people off going to hotels.

It wasn't just a diatribe written by the website's staff members: 2,000 parents had been asked their opinions, although I'm not sure in what context and I refuse to find out. But they must've been caught in a whingeing mood because they seemed determined to take popular culture personally. Ninety-three per cent thought that the typical comedically bungling TV dad doesn't accurately reflect what fathers contribute to families in real life. They were not then asked whether or not that's a problem – whether it is the job of a show such as The Simpsons to accurately reflect family life, whether such shows have ever implied they're an accurate reflection of anything at all and whether Homer Simpson accurately reflects the number of fingers most fathers have.

Had they been asked those things, I hope they would have responded along the lines of: "No, of course that's not a problem – it's just that you asked whether various characters in popular culture, which are clearly the product of comic exaggeration and in some cases surreal invention, were accurate reflections of reality and they're obviously not, so I said they weren't." But I doubt that's how it would have gone because 46% of those surveyed thought that these characters could make children believe that all dads are "useless" and 28% felt that these depictions amounted to a "very subtle form of discrimination". So they do seem quite het up about it, which I think is stupid and depressing.

My state of mind was not improved by the remarks with which Netmums' founder, Siobhan Freegard, accompanied the report. "It's never been harder to be a father – but good dads have never been more needed by their families," she said, which seems reasonable enough until you think about it for a second and realise that she's wrong on both counts. There have been many times in human history when it's been harder to be a father – during the Black Death, for example – and also many times when families have needed fathers more – the tens of thousands of years when they were expected to hunt and kill all the family's food springs to mind. Sorry if you think I'm being petty but, if she's going to claim that loads of comedies that people enjoy are corroding our society, she oughtn't to kick off with a historically inept statement.

She wasn't finished: "So it seems perverse we are telling men to step up and be involved, while running them down in the media." Who is this "we"? Whoever wrote The Flintstones? The Peppa Pig production team? She presumably counts herself among the people who tell men to "step up and be involved" – fair enough – but is she annoyed that she can't also vet all scripts for comedies and children's programmes for deviations from that message? Does she expect the culture to speak in unison? Does she believe that Fred Flintstone saying "Yabba‑dabba-do!" amounts to an advocacy of shouting gibberish? Maybe she thinks Miranda Hart's pratfalls undermine the good work of the Health and Safety Executive.

"Some people claim 'it's just a joke'," she continued, "but there's nothing amusing about taking away good role models for young boys." Yes there is. Once again, she's strayed into untruth. For example, when Homer Simpson says "Mmm… floor pie" on seeing a slice of pie on the floor, that is amusing and yet he is not being a positive role model. The negative role models Siobhan Freegard has commissioned a report to complain about do amusing things all the time.

What there is, for practical comedy-writing purposes, "nothing amusing about" is good role models: a caring, conscientious father who doesn't get into scrapes – that's the stuff of government information films, not funny programmes. And the "useless dad" may not be a fair reflection of society but, if it was complete invention, the characters wouldn't resonate. Accident-prone Daddy Pig, or Hugh Dennis's hapless character in Outnumbered, may not be representative examples of modern fatherhood but they obviously strike a chord or those shows wouldn't be watched by millions.

This report is at once joyless and opportunistic. It seeks to say something headline-grabbing and preachy to garner positive coverage for a website, and is content for some of the finest products of the noble human urge to amuse and entertain to be the victim. There are many things wrong with humanity but I'm fairly sure that funny sitcoms and cartoons about family life aren't among them.

But when Freegard says, "The type of jokes aimed at dads would be banned if they were aimed at women, ethnic minorities or religious groups", she has got a point – just not the one she thinks she's got. Men and fathers are so favoured in our society, the world is weighted so much to their advantage, that comedy writers can safely make them the perpetual butt of jokes. The fact that Homer Simpson is the funniest, most prominent and most popular character in that show says far more about continued male dominance of money and power in the west than his fecklessness or misfortunes say about the undervaluing of paternal effort.

Comedy is a misère bid – to be the biggest loser is to win. If a time comes when incompetent or hapless women are humorously depicted as often as their male equivalents, then the distorting fairground mirror of comedy might at last be reflecting a just world.

David Mitchell's memoir Back Story is out now in paperback