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.
Anyone who has spent time on old bulletin boards with overly loose moderation has seen this—one or two very busy and influential posters end up becoming the real subject of the board and most other posters either leave, lurk, or address the influential poster constantly.
You either end up with a small bulletin board that is either a cult or anti-cult around the poster, or a useless board where nobody talks, but just announces.

Now give that poster the power of the state and at least a thousand diehard gunmen.
A newspaper, publisher, shopping mall, all-you-can-eat buffet aren't going to customer service themselves into oblivion. "All You Can Eat" means I can put a tent in the dining room and be there 24/7 and vomit into a trough ten times a day, right?
The "censorship" crowd is saying "YES IT DOES MEAN THAT!"
But, the "it's a private company!!" crowd is making a similar error. If Twitter privately decided that what people really wanted were disinfobots and forced them onto your timelines and sent you constant texts of that content and buried malware in your browsers to ensure...
And ALL of that can be covered in a ToS that every single user here would have clicked on and agreed to without reading.

"But that's not a good idea..." except that "private companies can do what they want" short-circuits discussion of good or bad ideas.
We have a sense, some intuition, that there are good or bad decisions to be made. Parler and Gab and Telegraph pride themselves on "free speech" but go make an account and hassle the big posters—threaten them abstractly with a term in a gulag. You won't last. You won't.
Or if Twitter banned people for any of the millions of copyright/publicity infringements that take place on this site every day: quoting song lyrics, video snippets, celebrity headshots in avis, etc.

You wouldn't stand for it. You just wouldn't. But they're a private company!
Twitter can, as a private company, make your life as a user or even as someone who lives in a country full of users, absolutely miserable. Is that okay?

The "private company" crowd is saying "YES IT IS!"
But clearly it is not. So any discussion of Trump being barred is going to be unsatisfying unless it takes into account the dual concrete realities, which is one that he is the President and that he in particular has been the utter center of Twitter daily for many years.
And those two facts are why people are both objecting to his banning and applauding it.
So why is it okay? Because Trump is an increasingly unstable figure on this site and because he's president that virtual instability can leak very easily into the real world.

And Twitter has decided it would rather pursue business in a more rather than less stable environment.

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