I'm not too clear on the argument, I heard someone else make it, and forgot to save the video, but it has something to do with the fact that Twitter et al are not publishers, they're platforms, opening themselves up as "public forums for debate", in which case the first amendment is supposed to apply.
Also, plenty of private businesses in the past have put up signs saying "we reserve the right to refuse service", but it was apparently deemed that there was no legal basis for that.