Twitter is a public space, because being a public forum for speech is the essence of what Twitter does. It's privately owned, but like a privately owned mall, it is "open to the public" and therefore at least some free speech protections apply.

“the more an owner, for his advantage, opens up his property for use by the public in general, the more do his rights become circumscribed by the statutory and constitutional rights of those who use it.” (Marsh v. Alabama, 326 U.S. 501, 506 (1946).

The Supreme Court has since backtracked on the Marsh opinion somewhat, but some states such as California have ruled that reasonable exercise of speech and of petition rights on privately owned shopping malls are protected activities.

> It's privately owned, but like a privately owned mall, it is "open to the public" and therefore at least some free speech protections apply.

What are the Terms of Service (EULA) of a public shopping mall? What are they for Twitter?

When you click on "I agree" to the terms of software, or a website, what did you agree to? Where do you click "I agree" when visiting a shopping mall?

> Where do you click "I agree" when visiting a shopping mall?

There is usually an inconspicuously posted sign that indicates 'no loitering, no spitting, no foul language' etc. or they reserve the right to throw you out.

Twitter isn't a public forum for speech. You need to have an account to use Twitter, for which you agree to abide by Twitter's terms of service, in which Twitter reserves the right to moderate and ban content as they see fit. Marsh v. Alabama applied to physical property and AFAIK hasn't been definitively extended to online "properties" like Twitter.

In Manhattan Community Access v. Halleck[0], however, the Court ruled against the premise in regards to a public access television station, and maintained that the station remained a private actor despite being a "public forum."

[0]https://en.wikipedia.org/wiki/Manhattan_Community_Access_Cor...