Well I can understand him a bit since you called his all in while two over cards were on the flop (doesn't mean I would behave the same like him, yelling at you for 1 hour lol). He was the big favourite with his 2 pairs after the flop against your 1 small pair and yes you kinda "donked" him out by getting lucky on the turn with your set. So yes he has the right to be angry I guess, even that surely does not justify his behaviour in chat and is also quite ridiculous in my eyes when people do it lol.
Well such bad beats are part of poker I would say and if he can't handle it he should stop playing, that's my opinion.
But on the other hand think about it...if you would be the one pushing all in with AJ in this situation and someone calls with 66 and wins against you on the turn...wouldn't you think maybe as well: " Bah, what a donk !" ?
Edit: If he pushes all in every hand when you are in bb...he has to take the risk that you will call him eventually one time. And since he is your brother, I think you guys shouldn't quarrel about a thing like poker because it's not really worth it.