Primates in general tend to be opportunistic feeders, and in central Asia the opportunity for meat dwarfs one's ability to find figs or wild cherries growing on trees.  It's likely that due to the conditions of the region, the human tribes that may have been more varied in diet further south (middle east) would have become more carnivorous as plant food became more scarce.

In the middle east itself, river fish and wild fruits and vegetables would have been plentiful enough that it may not have even occurred to most tribes to attempt hunting game.