Proverbs 26:4-5 initially appears to give contradictory advice: "DO NOT ANSWER a fool according to his folly, or you will also be like him. ANSWER a fool according to his folly, that he not be wise in his own eyes." The keys to properly interpreting the apparently conflicting advice are the descriptions qualifying the imperative. The objective in the first case is engaging a fool without stooping to his level, using abusive language, character assassination, deflecting and blame-shifting. The goal should be rather narrowly correcting the fool over the issue in dispute, addressing raw facts without being abusive or judgmental of the fool. Of course the fool might still blow you off, but at least you're not communicating like the fool, according to his folly. And methodically sticking to the issue without being disrespectful is potentially corrective. The fool can no longer easily be right in his own eyes. The real issue then in these verses is how we converse with a fool, who would provoke a response in us that is verbally abusive, and abuse returned discredits whatever wisdom we might provide.
Instruct the Simple
This episode begins a survey of 5 types of fools described in Proverbs and Ecclesiastes. The first level fool most closely approximates the "fool" in English. The pethey fool refers to the simple and naive one, and unlike the other 4 fools, doesn't presume hatred or resistance to the knowledge of God. The pethey is credulous and uninformed and therefore vulnerable to the schemes of the wicked. The purpose of Proverbs is "to give prudence to the naive" (Proverbs 1:4) With respect to responding to the pethey, believers are strongly encouraged to instruct the simple with godly counsel. While saints are discouraged from responding to a "scoffer" (level 4 fool), Proverbs makes an exception in the event a scoffer's words might negatively impact the pethey. Bad counsel must be corrected: "when the scoffer is punished, the naive becomes wise." (Proverbs 21:11)