The issue is that youtube is not just 'someones site' just like facebook isn't just 'someones social media'. These platforms are ubiquitous these days, they are the de-facto place for content and thus become an important part of the forum on which we discuss.

If that forum is censored with too broad a stroke, that actually harms society. I think everyone can agree that too broad censorship is bad, and if it hits large swathes of society, is really bad.

The difference between youtube and hacker-news is scale and near-monopoly. There is also an important difference of human and machine censorship. Not a difference of appeal, but a difference of unintended consequences. A human censor will notice when certain rules have unintended and too broad of an effect. There is a baseline of human oversight built in because there is a human somewhere. Automated systems do not have this property, if they have rules that seemed reasonable but aren't in practice, or aren't anymore, the system won't notice.