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.
They’ve required a phone number every time I’ve tried to sign up. They don’t have it in the sign up flow - they wait until you try to sign in and won’t let you proceed without it.
I'm not sure if it's mandatory now either. The sign up button on the front page of Twitter.com says "Sign up with a phone number of email address". If you click on it, it defaults to a form with a name, phone number and date of birth, but there's a link titled "Use email instead" that changes it to name/email/date of birth.
It’s effectively mandatory. If you register an account without it, you will be banned within fifteen minutes, even if you do absolutely nothing, for “suspicious activity”. The only recourse? Handing over your phone number. Apparently that absolves you of any “suspicious activity”.
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.