I'm sorry this was added stress for you, AJ, and (not knowing exactly what was said by whom at what point) it does sound like she possibly responded a little more rudely than was necessary, but we have to remember that agents are human too and we don't know what else is going on. Perhaps your request for a "why?" came right after another author took a rejection very rudely, and she interpreted yours in the worst way, and especially if there was "back and forth" about it, she could have felt exactly the same about your responses as you did about hers.
It is a shame that she "liked" your pitch without intending to request. From what I see, it looks like she came about it in a roundabout way. Someone else mentioned the comp, and she found it and liked it. I do agree that once she found out about the #pitmad rules, it would've been better to respect the rules, rather than insisting that she can like what she wants to like. However, I think that at the point where she explained that she didn't mean to request it, the conversation probably should have ended. Telling you that she wouldn't have been interested because it was an angel story was more than she was entitled to do, and she probably thought she was being nice explaining why she wouldn't have looked at the book, even though you sent the query. You could probably have queried someone else at that agency at that point since this query was due to a mistake.
In general querying advice, it's not worth asking for a "why?" A rejection is a rejection, and if an agent doesn't like what your book's about, it does no good to ask them to justify not being into yours. Sometimes feedback can be helpful, but a matter of taste won't tell you anything.
In general twitching advice, it's probably better to tweet at an agent to ask what they want you to send if they didn't specify anywhere. If they meant to request, they will respond, enthusiastically. If they don't respond or post submission guidelines after the request, they probably weren't that interested.