I imagine they had staff members looking for any pretext, and also responded to social pressure. The obvious coordination of this action (Twitter was the only big holdout until now; the rest banned him on the same day) also raises significant questions. Bottom line, this was a test run and a precedent. They'll use this to coordinate banning more and more conservative voices. They will start on the very fringe and slowly work their way in, while leaving the left alone. The intended result will be to shift the Overton window of acceptable public opinion to the left and force people who won't parrot their dogma into a padded room on the internet -- they can yell but no one can hear them.
How to fight it is hard. I'm not reliant, here, on their platforms. But that means the audience is limited because the major audiences are on facebook, twitter, youtube, and google search.