I don't know. Can you explain, why should private companies be not allowed to discriminate, but allowed not to have free speech? In both cases you can say, well, if you're discriminated by a private company, you can always go to a different one.
I my view, the problem is that we don't want to force people (individuals) to non-discriminate or allow free speech. But institutions, it's another matter. If the institution has enough power, it can impede the rights of people.
So people asking for YT and such to respect freedom of speech are asking for them to be treated as institutions, something that is potentially more powerful than individuals. And they understand that freedom of speech (just like non-discrimination) is beneficial (for society) in any institution, not just government. After all, you can select a government too, by emigrating into a different country.