Twitter’s permanent ban on Trump’s personal account as well as other accounts cannot be attached by Trump. According to Twitter, it banned the former president for his inflammatory tweets after a pro-Trump mob stormed the Capitol while Congress convened in a joint session to preform thee administrative task of formally finalizing the electoral votes that the states had already certified, confirming Joe Biden as president. Twitter further suspended the accounts of main Trump supporters, including retired Gen. Michael Flynn, Trump lawyer Sidney Powell and supporters of the QAnon conspiracy theory. Other forums also disabled Trump’s accounts.
And Trump can do nothing about it. That is, free speech protection under the First Amendment to the US Constitution applies only to the government censoring speech. It does not apply to private companies.
Simply, there is no constitutional right to tweet or post on Facebook. All private companies, like a publisher of a newspaper, can determine what to allow on their platforms. Typically, they are contained in their “Terms of Service” provisions which users, by signing into the app, must agree to abide by. And if a user, such as Trump, violates those Terms of Service, Twitter, Facebook and others medias can block them from their platforms.
Twitter concluded, after Trump sent his tweets, that his messages could be viewed as inciting his followers to violence acts in urging his supporters to overturn the election because of his baseless claims of fraud and encouraging followers to commit violent acts against the government.
In short, First Amendment claims only pertain to censorship by the US government. Put another way, the First Amendment doesn’t compel any private company to give its customers the unfettered right to remain as customers of a company. If Trump, in Twitter’s opinion, violated its terms, he is out with no legal rcourse.