I was addressing your notion about businesses, "this legal loophole, businesses can do what they want". And I presumed you were actually talking about businesses, because a) you mentioned Twitter, a business, and b) UC Berkeley is not a business.
> sure that's legally true perhaps [...] it's not right and against the idea of the first amendment
No. No, no, no. The idea of the First Amendment is not that you are owed a platform. It's just that the government cannot stop you from saying what you want in public or with your own platform. It starts out with "Congress shall make no law" for a reason.
That is not the idea of the First Amendment. It is your idea of the First Amendment. It's a common one, but that doesn't make it the right one, or the only one.
Except the argument here is person X doesn't get to talk.
The argument is Berkeley can stop people talking they politically don't like (Or any other reason) because as a business they have every right to discriminate on political views.
And sure that's legally true perhaps, we all understand that, but it's not right and against the idea of the first amendment.
To argue it's ok for universities to censor speakers is a very scary point of view, and this is what you are doing by bringing in the straw person 'it's legally allowed'