Answer not a fool according to his folly, lest you be like him yourself.
Answer a fool according to his folly, lest he be wise in his own eyes.
Proverbs 26:4-5
The Claim: Blatant contradiction here. Verse 4 tells us not to answer a fool according to his folly, and verse 5 tells us to answer a fool according to his folly.
The Explanation: This would be a contradiction, but only if you ignore the second half of each sentence. However, each verse does not stop at the word folly, so let's examine each verse and see what they're really saying.
Answer not a fool according to his folly, lest you be like him yourself.
This verse serves as a warning statement. The proverb is warning us not to become like the fool ourselves. Now let's look at verse 5.
Answer a fool according to his folly, lest he be wise in his own eyes.
This verse is about correction. It's telling us to correct the fool, in an attempt to get them to see their own foolishness, so that the fool doesn't mistakenly think he is wise when he is actually foolish.
Now let's put both ideas together. We are to correct the fools so that they do not continue in their own foolishness thinking they are wise. At the same time we are to be careful when we attempt to correct the fool, and the fool responds back with more foolishness. Verse 4 is warning us not to get caught up with the fool's folly, and verse 5 is telling us to correct the fool's folly. There is no contradiction here.