You're confusing yourself. Let me use reductio ad absurdum to point out how your logic is self-defeating. Please understand, I'm not ridiculing you, just pointing out the logical fallacy. Try this formulation...
Isn't hating "hate", in itself, hateful? Why, then, it follows that we should love "hate" in order to be loving! Hate people: it's what loving people would do!
There is a moral equivalence here that's wrong. Despising things that are evil isn't in itself evil, merely because you're employing a word or sentiment normally associated with evil. It's the loaded meaning of the words "despise" and "intolerant" that's tripping you up. Try the word "embrace" instead and things become much clearer.
Example: Isn't failing to embrace intolerance intolerant? No, it's the very opposite.