> if you exercise your right to offend people in my establishment, I have the right to toss you onto the pavement

not anymore (if you are implying physical removal). you can't even apprehend shoplifters anymore without getting sued.

Purely literally, yes, you're correct, you can neither physically remove someone nor physically restrain someone, and this is a good thing, as the state has a monopoly on use of force.

If you only "metaphorically" toss someone onto the pavement, though (tell them to leave the premises), you're fine, and can have the group who has a monopoly on force enforce that request if necessary.

Metaphorically, because we're really talking about whether "liberty" implies a "right to offend people" that precludes Twitch from being able to ban any account for any users' behavior. It does not. Especially not for the kind of egregious reasons they're stating.

> this is a good thing, as the state has a monopoly on use of force

i disagree that its a good thing. The threat of a minor altercation from property owners helps maintain stability (emphasis on minor).

And the state having a monopoly on violence changes the dynamic of property, where the government can take whatever it wants from me (even my children) if they want to dream up a reason.

>And the state having a monopoly on violence changes the dynamic of property, where the government can take whatever it wants from me (even my children) if they want to dream up a reason.

On the other hand, without the state having a monopoly on violence, anyone has the right to take whatever they want from you, given sufficient force.