Jeremy Corbyn’s intervention in the EU debate was notable, but it wasn’t what journalists were talking about after his speech. The hot topic was the chorus of boos for their presence, and the hisses for the BBC’s Laura Kuenssberg.

That followed hot on the heels of the Vice documentary about Jeremy Corbyn, in which the Labour leader complains extensively about bias in the press. One of the things he has learned as leader, he says, is “how shallow, facile and ill-informed many of the supposed well-informed major commentators are in our media”. I suppose I should just be glad he reads my columns.

To be honest I didn’t really understand why so many journalists got so sensitive about it. Surely the role of the media is to hold politicians to account, not to be liked by them. You might even say disgruntled politicians are a symptom of journalists doing their jobs properly. I won’t shed a tear for the end of those cosy relationships between hacks and MPs, which – at the extreme end of the spectrum – involve political leaders becoming godfathers to the children of media moguls.

And when it comes to media bias, Corbyn has a point. I went to John McDonnell’s New Economics conference on 21 May. It was an impressive and substantial event, at which dozens of world-renowned figures came together to debate a departure from the neoliberal economics that has dominated Britain for the past 35 years. And what was the main topic of media coverage the next day? The fact that a Labour party staffer accidentally sent members an email that began with the phrase “Dear Firstname”.

This was facile on behalf of the press, and readers deserve better. Indeed, in a response to the Vice documentary, the Sun (apparently without irony) rebuffed the charge that the media give Corbyn a hard time by describing him as “hapless” and “snarling”.

But it is at this point that I part company with lots of other Corbyn supporters. Since he won the leadership last year I have spoken with many who insist the media is so unfairly biased against him that it is simply not worth engaging with, except to chastise certain journalists for bad reporting. The solution, these Corbyn supporters say, is to connect with the public in other ways: by utilising social media, or simply refusing to cooperate with the public school dorm culture of the lobby.

The question of how Corbyn maintains his integrity while succeeding in a deeply cynical system is a tough one to answer

I sympathise with this position, but it seems unfeasible. For one thing, most people still consume news via the mainstream media. A 2013 Ofcom report found that 78% of people rely on television as their main source of news, compared with 19% who use Facebook and 10% who use Twitter. Crucially, less than a third of respondents regarded Twitter as trustworthy. If Corbyn were to circumvent the mainstream media, he would lose the opportunity to communicate with a significant chunk of the British public.

More importantly though, I think complaining about media bias fundamentally misunderstands the way Westminster politics works. It’s easy to mistake parliament for a civilised place: the archaic traditions, opulent settings and glut of privately educated old men suggest as much. I imagine if most people were asked to compare Westminster to another institution they might choose a court of law or a university. But the truth is, Westminster is more like a bear pit. Those within it must do whatever they can to survive, they cannot display any signs of weakness, and the whole thing unfolds as a rather sordid public spectacle.

If someone chooses to enter frontline politics, as Corbyn has, they are climbing into the bear pit. Once they’ve done that, they can’t just stand there complaining it’s not the gentlemanly pursuit they hoped it would be, because they’ll get eaten alive. Once you’re in, the only choice you have is to fight for your life, even if – as in Corbyn’s case – the odds are unfairly weighted against you.

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Practically speaking, this means designing a media strategy involving a few key messages about the state of the economy and repeating them endlessly until they bore you to tears. It means leaping upon all the mainstream media platforms you possibly can, no matter how odious you regard them to be. It means identifying the key demographics you need to win over for electoral success and relentlessly pursuing them. It means taking advantage of the government’s weaknesses at every opportunity. And it also means saying things you’d rather not say, and self-censoring on occasion, because you’re conscious of how your words might be manipulated by others to undermine your overarching aims.

Of course, this is harder for Corbyn than it sounds. He has been ushered into power by people who like him precisely because he refuses to take part in Westminster bloodsports. So the question of how he maintains his integrity while also succeeding in a deeply cynical system is a tough one to answer.

And as someone who has been watching his team at close range, I suspect that finding the time to design a long-term media strategy has been sabotaged by the immediate firefighting required to stymie the constant threat of bad headlines and internal coups. In that respect Corbyn’s camp are doing a better job than they have been given credit for.

Even so, the media is the wrong target here. Yes, it is part of the establishment. But it is also a conduit through which Corbyn can communicate with millions of people. To that end, he must focus on using it to his advantage. He’s right to feel aggrieved that the media isn’t giving him a fair hearing, but the Westminster bear pit isn’t fair. And right now, accepting the reality of the situation is the best chance Corbyn has of surviving it.