For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
Frederic A Parker
A quick note about the book of Proverbs – a special target for skeptics. A proverb, by definition is a statement of general truth or advice, an observation about real life. There are a few commands in Proverbs (they start with “Do not”). However, most Proverbs are NOT commands or rules, but observations. They tell us, “do this and this will result,” or “do that and something else will result.” People who try to make Proverbs into a rule book run into serious difficulties.
Jennifer Rothnie
In this case one of the two verses do start with "Do not", or rather the Hebrew equivalent, which is why it comes off as contradicting commands. ("Answer" and "Answer not").
It is one of my favorite pairs of proverbs, actually, as the seeming contradiction is no real contradiction; it is simply saying that you cannot win when arguing with a fool! If you answer according to his folly, then he may listen to you but you have now stooped to the level of a fool yourself. If you do not answer according to his folly, then the fool thinks he has won.
The solution is not really to pick one or the other according to the outcome you feel will be optimal, as in either case the outcome is not optimal. Rather, the best way is to not directly engage the argument at all. Jesus was very good at sidestepping these meaningless arguments by either asking a question (Matt 21:13), telling a parable, talking on a related topic (Luke 13:23-30), saying nothing at all (Luke 23:9), etc.
David Nochella
I light of the breath of scripture there is a time for everything under the sun so choose wisely when or when not to speak to a fool.