Do you have any evidence the "left wing" is in any more of an echo chamber than the right wing? Is this just personal observation or do you have something more to point to?
Presumably the right-wing are just as capable (and historically have been the aggressor often), but the left have mastered it as a form recently.
As for providing some evidence of cancel culture and deplatforming, somebody would have to have been living on Mars (or have blinkers) to have missed the odious practices (as evidenced in the OP!) that the terms were invented for, and I'm not sure me spending my time googling and linking examples is going to help in that case.