What's the reason?
Because people are, well, human. With emotions, that sometimes overrides common sense.
How to come out from this situation?
To prevent it from happening in the first place, just think twice before commenting on bad answer after you downvote it. Of course it's good and desireable to comment, but if your reputation isn't really high, and you're afraid downvote will be meaningful and hurting, just don't comment. Or at least try to be gentle when doing so, e.g. don't throw "-1, answer is wrong" but rather explain why it's wrong in a gentle way.
After it already happened, there's not much you can do, as others here already said. Since you can't be sure the one you downvoted really downvoted you, commenting on their answer about it won't be a good idea. The only way I can see, assuming you both have enough reputation, is starting a new chat room with that user, and in there start with something like "Do you want to discuss your answer?", which might lead to friendly outcome, and possibly removal of the revenge vote, if that was really the case.