here is what I know so far.
1) the far right organized a hate rally.
2) the antifa and blm folks came to counter protest
3) both sides brought weapons and therefore both planned on physical violence.
4) a lot of people got hurt , one got killed. people hurt were on both sides of the extreme aisle.
now you suddenly expect our president to take sides and only condemn one form of extreme violence.
I will call bull

on that.
I do think your right though the reason the left is trying to make the wording an issue is for the political reason you mentioned. its always a political game.