There are many possible reasons. The answeree (respondee? respondent? magic healer?)...
- ... is a newer user unfamiliar with the "way it's supposed to work"
- ... is relatively inexperienced but knows enough to answer a question most experienced users would throw RTFM you derelict swine at (an alternative to this crew is the LMGTFY, you lazy excuse for a human, because manuals are so passé)
- ... is answering before most of the downvotes come in
- ... sympathizes
- ... just wants to help
- ... is having a good day and at that moment is feeling generous/charitable
- ... began writing the answer before the downvotes started flowing, hence missing the warning
- ... doesn't care about the downvotes (the Fascists! argument)
- ... is answering because of the downvotes (the B#st#rds! argument)
- ... mistakes the answer field for a comment field (see #1 and #2 above)
- ... is coming from a different point of view and considers the downvotes as meaningless commentary re: the question
- ... feels they understand what the question is really after
- ... doesn't subscribe to your doctrine/belief system/Sports Illustrated
- ... has bad intentions
- ... didn't take a shower this morning
- ... didn't read this question
- ... was late to class
- ... swallowed a bug
- ... has never seen Deer Hunter
- ... has seen the "Needs More Cowbell" skit (but doesn't get it)
- ... [fill in the blank, but don't taze me bro!]
I think it's also useful to think about the reasons a person (I assume they're people, guess they could be... something else) downvotes a question. I don't have a list ready for that side of it, but I do think there are many different reasons (claiming reason always plays into the decision to downvote is something I don't believe) it happens. So it can go both ways, with multiple competing viewpoints, personalities, objectives, grudges, bad moods, lack of [fill in the blank], too much (chutzpah? nerve? bad breath?), etc.
I suspect (but can't prove) I have seen questions that suffered from drive-by pile-ons, where an initial perception of the question caused several (probably "well-meaning") downvotes to be given, with several loud and highly visible comments possibly influencing some members negatively, leading some (nameless, faceless) users to exercise their finger without exercising their brain.
I've done it myself, but I know (know) I'm not the only one who's done this (and I admit it was a mistake on my part a few times, other times the question was sufficiently modified quickly enough to eliminate the problem). If you've downvoted more than a few questions, and especially if you frequently downvote questions, but still think this doesn't apply to you ("Who, me?" Yes, you.), I propose you have not been considering or paying enough attention.
It's not illegal/immoral/extra-judicial to answer a question in which "some people" (they will remain unnamed) felt confident enough to downvote, no matter what we see in the question itself indicating the questioner's intentions ("r u codez? hw 2 bild $$ mkng app. answr wcode plz" is not always the case).
Personally, I don't let it get it to me, although sometimes I'm miffed at it too. C'est la vie!
Just my two cents. You have change for a dollar?