that is even confirmed in book 7: don't call her a Mudblood. Why would he care if he hated Hermione?
Well....I agree that he never hated her, nor wished her ill. But his reaction to Mudblood in book 7 had much more to do with himself than the target of the comment, didn't it?
Severus' teaching from that book doesn't mean teaching morals and compassion. It means teaching tactics and winning
But that's what I'm trying to say. Hermione's refusal to consider the long-term ramifications of her actions has nothing to do here with morals and compassion. It has everything to do with tactics and winning, part of which is not making any more enemies than necessary as well as giving people a graceful way to back down (or in the language of The Art of War, a safe way to retreat when it's not essential to crush them, because then you have not spent any of your resources, a/k/a potential casualties).