One reason it really is difficult for some to wrap their heads around why it's fine that Trump is banned from Twitter is because "a private company can do what it wants" is an unsatisfying answer. And it really is unsatisfying, but it is also not the actual reason why it's fine.
The reason why it is fine is basic to cybernetics: the most unstable element of any system has the most influence over the system. Not control necessarily, but influence.
Trump is less *stable* in his messaging than Ayatollahs and the Chinese government, leaving aside the object-level horror of messages. He's less restrained than pornbots, and more powerful than a run-of-the-mill death threatener.
He's also the absolute center of world news and attention, every day.
Both the "censorship" and "private companies" crowds are arguing for a static abstraction in the face of a concrete dynamic.
And the concrete dynamic is that Twitter, headquartered and publicly traded in the US, with many employees who are difficult to easily replace, is being made unstable as both a communication venue and a company, by Trump's continued presence on the site.