I know Harry is just a kid, but his reaction towards unicorns don't seem very rational to me. Remember, Harry became vegetarian for a while when he was afraid animals could be sentient. And now, he speaks about massively killing unicorns, magical creatures whose sentient status isn't very clear (like with phoenix), for a "temporary" stop of death at a cost of "permanent side-effects", without inquiring how temporary temporary is, what are those side-effects, and how sentient unicorns are. Without measuring those three parameters, there is no way to know if utility(killing unicorns in St Mungo) is positive or negative.