Proverbs 26:4

4 Answer not the fool according to his folly, Lest thou thyself also become like unto him. After, or according to his folly, is here equivalent to recognising the foolish supposition and the foolish object of his question, and thereupon considering it, as if, e.g., he asked why the ignorant man was happier than the man who had much knowledge, or how one may acquire the art of making gold; for "a fool can ask more than ten wise men can answer." He who recognises such questions as justifiable, and thus sanctions them, places himself on an equality with the fool, and easily himself becomes one. The proverb that follows affirms apparently the direct contrary:

See here the noble security of the scripture-style, which seems to contradict itself, but really does not. Wise men have need to be directed how to deal with fools; and they have never more need of wisdom than in dealing with such, to know when to keep silence and when to speak, for there may be a time for both. 1. In some cases a wise man will not set his wit to that of a fool so far as to answer him according to his folly "If he boast of himself, do not answer him by boasting of thyself. If he rail and talk passionately, do not thou rail and talk passionately too. If he tell one great lie, do not thou tell another to match it. If he calumniate thy friends, do not thou calumniate his. If he banter, do not answer him in his own language, lest thou be like him, even thou, who knowest better things, who hast more sense, and hast been better taught." 2. Yet, in other cases, a wise man will use his wisdom for the conviction of a fool, when, by taking notice of what he says, there may be hopes of doing good, or at least preventing further, mischief, either to himself or others. "If thou have reason to think that thy silence will be deemed an evidence of the weakness of thy cause, or of thy own weakness, in such a case answer him, and let it be an answer ad hominem - to the man, beat him at his own weapons, and that will be an answer ad rem - to the point, or as good as one. If he offer any thing that looks like an argument, an answer that, and suit thy answer to his case. If he think, because thou dost not answer him, that what he says is unanswerable, then give him an answer, lest he be wise in his own conceit and boast of a victory." For (Luk 7:35) Wisdom's children must justify her.

26:4-5 Proverbs are often context sensitive. Whether or not to answer the foolish arguments of fools depends on what kind of fool and what kind of situation.