Regardless of if his or the company's official claims, when network effects centralize virtually everyone into a small number of platforms, it becomes a defacto utility. This has wide ranging and damaging effects on actual democracy. I don't particularly care what statements Twitter has made, if their platform has such wide ranging negative effects then it becomes an issue that needs to be addressed. How that's addressed is another question, but being a private entity doesn't magically free them from accountability of the negative effects of their platform.
Twitter is a business and it literally has nothing to do with democracy at all. Using twitter is a personal choice, if you don't like it, don't use it. That's the solution. Your perception of their business being negative or even positive is neither here nor there.
Once that was done, they noticed that people aren't free to speak & won't use a platform where they are constantly under attack from racists, sexists & harassers. As a private entity, Twitter cared more about people feeling comfortable participating than it did about other people's "right" to bully, harass or send dick pics.
They also realized that if they kept letting their platform be used to radicalize terrorists, the government was going to shut them down because they were harmful to the community. It's also possible that they didn't feel great about helping people murder people they hated. Repeatedly.
By that point Jack had realized that "Free Speech" is a lot more nuanced than he imagined as a 29 year old with no background in sociology, philosophy, law or political science. Jack still believes in freedom: he just knows now, experimentally, that you can't achieve that by letting might make right.
Nobody is arguing that constitutional rights directly apply here. They're arguing that free speech is important, especially when the government has been pushing around that private company: https://www.forbes.com/sites/emmawoollacott/2021/07/15/gover...
"common limitations or boundaries to freedom of speech relate to libel, slander, obscenity, pornography, sedition, incitement, fighting words, classified information, copyright violation, trade secrets, food labeling, non-disclosure agreements, the right to privacy, dignity, the right to be forgotten, public security, and perjury."