The crime was inciting an insurrection. The president was not charged due to partisan politics, no president has ever actually been voted out by the Senate of their own party (correct me if I'm wrong), but historically this has been the most votes received from their party. It's recommended to understand both the background and the event on January 6th to get a clear picture, including attempts to overturn the election. More details here: https://en.m.wikipedia.org/wiki/Second_impeachment_of_Donald...
Twitter is responsible for moderating the users their platform, regardless of whether they are free speech purists. You cannot let your users plot crimes. That's why sites like Silk Road and AlphaBay were shut down.