This Supreme Court case is about whether social media sites can be forced to host users' speech, not whether the sites are liable for the users' speech. On the latter subject though...
> I don't think they should be able to have it both ways.
> Social media companies have speech? If they have speech then why aren't they liable for that speech?
The state governments trying hold social media sites liable for users' harmful speech want to "have it both ways": Hold social media sites liable only for certain speech, yet pretend that the proposed laws instituting that liability regulate conduct without regulating speech.
Most of the speech targeted by proposed third-party liability laws such as KOSA is protected by the First Amendment (LGBTQ information, eating disorder discussions, body image posts, etc.). Without some evidence of causal harm on a case-by-case basis, not even first-party liability - liability on the users who posted the speech on social media - would pass the First Amendment, and third-party liability would not apply in such cases. But assume that first-party liability would apply. What about third-party liability for social media sites' moderation of user speech?
The First Amendment can prohibit both direct and indirect restrictions on protected speech. Strict scrutiny [1] requires laws impacting constitutional rights to use the methods least restrictive of those rights. Moderation of user posts by social media sites is a First Amendment right, just as posting by users of social media sites is a First Amendment right. Holding the social media site liable for First-Amendment-protected user speech violates strict scrutiny because a method less restrictive of protected speech is holding the respective users liable for posting that speech.
[1] https://en.wikipedia.org/wiki/Strict_scrutiny
And before anyone brings up republication liability on newspapers: defamation is unprotected speech. Defamation does not have First Amendment protection. But holding a party liable for defamation in the US requires that the party distributing the allegedly defamatory speech know that the speech exists. Newspapers tend to check even their op eds before deciding whether they should stay. But the humans managing social media sites don't necessarily know that any particular post exists, especially when the moderation system includes automatic processes. Section 230 declares that social media sites are not liable for defamation even if they know about it. Without Section 230 in place, social media sites would have an incentive to stop manually moderating posts, because you can't know about specific defamatory posts if you don't look at them.