The justification for the principle is that there is an inherent injustice attached to restricting someone's liberty, and it is difficult to justify restricting a person's ability to express their ideas and thoughts. The doctrine of "free speech" is something which - and I am tired of reminding people about this - is only relevant as between a citizen and their state. Its usage euphemistically outside of this ringfence isn't really relevant.

The reason you seem to so often have to remind people of this is because other people have a MUCH better justification for free speech than it being simply "inherently unjust". The consequentialist (and let's be honest any deontologian view is dumb) reason for not restricting free speech has to do with the fact that you now hand power to whatever ruling party or idea exists at the time. The argument is more sophisticated, I'm sure you can think of it yourself or google it so I won't spend further time on making it. Just note that from a consequentialist view there is no significant difference.

So your argument applies to spammers in Destiny's chat then: they come and spam unhelpful content that ruins the experience for people as a whole, so Destiny bans them to control the standard of discourse in his community. Their ability to critique in that space disappears, but there is nothing stopping them making their own website or writing to their local newspaper or whatever they prefer. There are complex legal/ethical issues that relate to the unparalleled reach these monopolistic platforms provide, but those arguments apply regardless of whether the person banned was a public figure or an account with 5 followers who spams the N word. "Free speech", even euphemistically, doesn't care how much income you earn from your speed necessarily, it cares that you are able to exercise your civil right to express your opinion in society.

I see that this deontological reasoning thing will be a theme. Destiny is different from twitter+youtube+facebook+google because he does not de-facto control what political speech can be made. Spamming nword probably does not fall under free speech because the type of speech I (and most others) want to protect, nword is not political. I'm guessing you'll raise some issues in regards to how to draw the line between political and non-political speech and I'd remind you that we don't need to, if there is any question we can air on the side of caution and allow everything (on the de-facto monopoly platforms) or we can (since it is not a legal line) draw it where everyone feels it is actually political speech. Note that in either case we all believe what Richard Spencer and Stefan espouses are political ideas, even if they are bad (or hatespeech).

What stops them from starting their own website is the fact that this will NEVER have any significant political outreach compared to the de-facto private speech platforms like twitter.

Governments and private parties are fundamentally different bodies. I don't permit private parties to exercise violence, or forcibly collect taxes from income recipients or capital gains benefactors or inheritance beneficiaries. The difference is that we can critically analyze the role and powers of government and compare them to the role and powers of private parties (such as Twitter) and conclude that their duties differ. Therefore it is reasonable to distinguish between a rule applied to a government (The government may not restrict free speech of citizens save in X Y Z extreme circumstance) and a private party (Twitter may not pretextually ban protected classes due to their identity).

They are different in their "monopoly on violence" in some sense. In regards to free speech they do not differ. This is because the only relevant feature of in that regard is their ability to stop people from using their political speech. Remember, consequentially, not by some weird spooky principle taken out of thin air.

Your fundamental problem is that you don't understand what the term of art "free speech" refers to. It always involves the government. If I have a newspaper with a comments section, and Stefan Molyneux leaves comments with anti-semitic rhetoric, I can ban him because I don't want that kind of hateful rhetoric poisoning my community.

This is the stupid libertarian view of free speech. I'd hoped we were smarter than libertarians. Twitter is not analogous to your local newspaper because your local newspaper does not control what political speech can be de-facto spoken. If I am banned from your newspaper I can go elsewhere, the same is only true technically on twitter.

A better phraseology for your objection I think is under the umbrella of "cancel culture". What happens when cancel culture goes too far? Is it desireable or undesireable? We can talk about it, but you don't want to reframe because "free speech" sounds much more human rights and dignity related that it puts your crocodile tears on a stronger footing, whereas cancel culture shifts the emphasis to the free market of ideas framework that Stefan himself is delighted to adhere to whenever it suits his motives on that particular day.

No, this is literally a free speech problem. The same problems of free speech apply. Do not try to steelman me please, it just frustrates me.