Too tired to finish reading now, but I'll try to give a better overview tomorrow.
There are three causes of action. The first is breach of contract. This is treating the Terms of Service and other associated arglebargle as a binding contract, which it more or less is. Your presence on the platform is the consideration you give in return for the promises of Twitter to do what they're doing.
I don't think this is strong since as with most such platforms, they reserve the right to kick you off for a broad range of behaviors more or less up to them. I don't really see a precedent that an ISP is generally liable for kicking you off a free service.
The second is promissory estoppel, a more elusive cause of action, and is based on the general fact that Twitter has, since its existence, held itself out as some kind of free speech platform welcoming all and that short of illegal behavior like promoting terrorism or very limited kinds of hate speech, you can expect to be able to say what you want.
As a result of this promise, people have devoted a lot of spare time to Twitter pursuits, and yet, that promise is complete bullshit. They got in this monopolistic position on false pretenses by lying to people, and it's actually a platform that is pushing a very specific agenda, and if you are not aboard the troon train and willing to pretend men are women, you're not welcome.
Again, I don't think much of this from a legal perspective. I don't see it succeeding. However, Twitter looks like shit if they make the argument in their defense that they were basically lying but it's okay to lie, and yes, they really are a one opinion only allowed forum, not a free speech platform, and if you are a conservative, get off.
Their defense, and it's legally sound, is they're basically a pack of liars, their whole premise for existing is bullshit, they have an agenda and they're pushing it, and they're legally entitled to do that. Don't like it? Leave.
Their defense is to tell a good chunk of their userbase to fuck off and go somewhere else.
The third and actually most interesting cause of action from a legal perspective, and the one I think is most likely to survive a motion to dismiss is this:
Violation of Unfair Competition Law – Bus. & Prof. Code § 17200, et seq.
Now there's a mouth full. What exactly is that, you might ask.
Well, Dhillon is happy to say:
"Under the Unfair Competition Law (UCL), “[a]ny person who engages, has engaged, or proposes to engage in unfair competition may be enjoined in any court of competent jurisdiction.” Civ. Code § 17203. Unfair competition is defined as “any unlawful, unfair or fraudulent business act or practice and unfair, deceptive, untrue or misleading advertising.” Civ. Code § 17200.
Advertising is nearly any public statement a company makes encouraging people to use their product, either on its own merits or as compared to some available competitor.
Twitter routinely makes public statements of this sort and has for years:
“1. Twitter stands for freedom of expression for everyone.
2. We do not take sides. We show sides. Every side.
3. We treat everyone equally: the same Twitter Rules apply to all.
4. You have the right to express yourself on Twitter if you adhere to these rules.”
This statement is intended to get people to use Twitter, that is, to become their customers. This is advertising.
It is also, as we all know, an outright fucking lie.
Quite often, unfair competition/false advertising claims like this are pursued by competitors who allege that their customers have been poached by false advertising and they're entitled to compensation for lost profits and injunctive relief prohibiting future such claims.
However, in this case the plaintiff is claiming to be a deceived customer who relied upon their false advertising in order to become a customer and has thereby lost something of value, essentially treating the statute as a consumer fraud statute. Dhillon appears to believe California allows this and makes apt looking arguments in favor of that view.
Usually, you lead with your strongest claim and end with the flimsier ones. In this case, Dhillon has led with the headline getting claims, despite the fact that (IMO) they do not seem likely to succeed, while the oddball final claim is the one that seems like it might actually have a shot.