Because shutting down extremist accounts ends violent extremism
For Twitter, you can assume that this is not so much about pushing agendas or silencing voices (or ending extremism). This is about making sure Twitter doesn't become an unpleasant place to be. If people stop going there because it sucks because it's full of lulz nazi eggs shouting caps-locked slurs at them, that hurts Twitter right in the pocketbook.
Argue all you want about Twitter's responsibility to defend free speech, but ultimately they're a business, and a business can't be perceived as though they're looking the other way while extremists harass and threaten their user base.