It's really easy to get banned from Twitter (or at least muted for a few days). Look up the topics that Jack doesn't like, and make a few controversial posts. They don't have to be rude or anything, as long as they're contrary to his point of view.
Just ask Azealia Banks or Jane Oranika or xoxbea -- oh, wait, xoxbea DIDN'T get banned, but hopefully got a visit from Secret Service.
"Let me offer you my definition of social justice: I keep what I earn and you keep what you earn. Do you disagree? Well then tell me how much of what I earn belongs to you - and why?” ~Walter Williams