To put it another way, regardless of whether you agree with their logic, they've provided you with it: 'SJW' came from the right wing and describes progressives, therefore it is derogatory. If they have the facts wrong, demonstrate that and perhaps they will change their point of view.
The phrase originated in the late 20th century as a neutral or positive term for people engaged in social justice activism.[1] In 2011, when the term first appeared on Twitter, it changed from a primarily positive term to an overwhelmingly negative one
As for your overall point, for an argument to be sound, its propositions have to be true and the logic has to valid. Even if the poster was right about the origin of the term, they failed to support their conclusion; namely that we should stop using the term SJW. Their conclusion wouldn’t follow from their premises even if they were true because the argument is fallacious (genetic fallacy, as I said).
As it happens, they were both factually and logically incorrect, and they papered over the flaws in their reasoning with manipulative rhetoric. To my mind, that’s exactly the sort of discourse that should be called out as harmful to reasonable conversation.
Further note that whether the term “SJW” originated with the far right — it didn’t — is irrelevant to its usefulness or accuracy (genetic fallacy).
The hyperbolic and fallacious arguments are to be found in the first poster’s comments.