If animals trying to attack your character, they take 1 piece of meat from your inventory. If succesfully, well-fed animal won't notice "animal trainer" anymore, except of being attacked by him. If no food - perk isn't work.
This perk can't remove dmg from first attack even if meat avialable, because wild animals bites the hand that feed them 
I think it has nothing with petting followers, it's about giving animals food for them to ignore you if u arent hostile, no?
Still it's not the feature i'd personally like to see before some improvements of balance and content, as always.
Hm, also it could be used as a point where to bait your enemies so these npc will attack them, but only if you success in baiting. Then it will become MEAT-BAIT-FIGHTS.