It is privately owned, but it acts as a public square. For the same reasons that we defend the right to Free Speech at the public level, we should push the platforms that act as public squares to guarantee Free Speech.
We have already seen how limiting Free Speech, in the name of fighting "disinformation", can be abused.
This is the kind censoring I've personally been subjected to:
https://news.ycombinator.com/item?id=28411734
Meanwhile on Twitter, the "fact-checkers" are now taking it upon themselves to try to discredit tweets that make the leading personalities of the political left look bad:
This is abuse of the allegedly impartial fact-checking process for clearly ideological ends.
Another demonstration of this is the Facebook "whistleblower". She explained that she was motivated to blow the whistle after one of her friends was, in her words, radicalized, through Facebook. Of course she doesn't consider herself, a lifelong "ally" and supporter of far-left causes, who worked on a search feature allowing Pinterest users to search by skin tone - in order to discriminate in favor of people of certain colors - radicalized. Because that's pro-establishment radicalism.
Yet another would be Twitter's policy of banning people who refer to males who present as women with male gender pronouns. This moderation policy enforces left-wing ideological values, like the idea that gender is a property that is self-chosen, and for something that acts as a public square to push left wing ideology via censorship is deeply inappropriate.
Like Glenn Greenwald said:
https://twitter.com/ggreenwald/status/1434854149087182848
>>The entire "anti-disinformation"/"anti-extremism" industry is a gigantic fraud, funded by the same tiny handful of billionaires, governments and NGOs: a scam to control discourse while feigning neutral, non-ideological goals to battle "disinformation"
The fight against disinformation is really a fight to stifle dissent against the establishment and its official ideology, which I prefer to call Diversity, Inclusivity and Equity (DIE).