As became familiar in the Harry Potter series, our hero emerges from whatever mess he’s been in – daunted, hurting, but undefeated – to find a kindly mentor-figure ready to explain everything.
Or not, as the case may be. Knowing the whole story (or at least as much of it as one can glean from reading the books), Dumbledore’s “answers” to Harry’s questions are annoying. I suspect Dumbledore’s problem is that he doesn’t understand people as well as he thinks he does*. His answers have that annoying sense of being true and complete, but actually leaving out details that are important; not realising that a section of the picture doesn’t make the same sense without the rest (so people may come to different conclusions based on incomplete evidence).
For example “he hated your father when they were at school together, rather like you and Malfoy. Then your father saved his life” (paraphrasing) barely scratches the surface of Snape’s particular venom towards Harry. It’s like he’s forgotten (or is underestimating) the romantic rivalry. He always seems to assume Snape will somehow “get over”, or “rise above” his hatred of Harry.
Perhaps it’s related to the way he assumes the best of people – that they are able to be as sensible, wise, and capable as himself, given half a chance (and yet he doesn’t trust them with information that might allow them to do so – go figure). Or maybe is just a bit mad.
* I should note that he does understand them very well, but he still makes mistakes and assumptions that cause problems – usually for Harry.