I think what's being ground up against here is that weapon proficiencies tied to race inherently don't make sense in most cases, so arguing lore justifications are going to work.
We have this in Real Life. Several countries have mandatory military service which includes training with very specific weapons. Several U.S. states value hunting in a way that leads to either rifle and/or shotgun proficiencies being a near universal skill there.
Yes, countries. Not races. Would the elves of one nation in the south have the same mandatory training as one in the snowy north? Would a human in the big city have the same training as one in the country? It really doesn't work once you try and think about races as anything beyond stereotypes of themselves. Even racial ASIs, much as I think there are better ways to show racial differences, can at least be argued to denote some sort of innate, majorly biological difference.
We do have those exact differences in the 'subraces' which are the equivalent of nations. Drow and Wood Elves have different racial weapons. Shield/Mountain Dwarves have armor training that their Hill/Gold counterparts do not.
If you don't want to compare races to nations, but species instead, then we have that same real life equivalent. Humans have a racial predilection towards hand wielded weapons, while canines prefer natural biting weapons, and mantis shrimp prefer unarmed blunt or piercing strikes.
