Me neither, but I signed up back in the Dark Ages. Pretty sure that if you sign up today there's no way to avoid giving them a phone no. For me that would be reason enough to just say no, but most people give more fucks about these things than I do.
I wrote to support that I would rather not use Twitter than giving my number. They unlocked my account.
It blocks you from doing anything unless and until you give them your phone number.
Give it a go in an incognito tab now, you’ll see. It’s intentionally deceptive, and they’ve shown time and time again they can’t be trusted with the data.