Bosses enrage if you kill them too slowly - you don't have unlimited time to down them (otherwise you could just take 3 healers and a tank and never fail.) Just kill him more quickly (so improve gear/rotations for your DPS.)
That isn't supposed to be accurate for story mode (flashpoints). I don't know if the concept was changed for SM LI or not, or if it's a bug though. But for all other flashpoints at least, there are not supposed to be enrages.