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.
There are two ways of responding to one who denies the basic truth (of God) - answer him by the truth (Do not answer a fool according to his foolishness). Christian apologetic must begin with presenting the truth as revealed by God from the Scriptures. But there is also a place of demolishing the pedestal of the fool by showing the folly of his position. This is why when presenting the truth we expound the Scriptures and then we go on to show what it is not. The fool is one who says in his heart there is no God (Psalm 14:1; 53:1) You've to define terms as they're used in Scripture.
I want to take more time to explain them to you - for you need it. This is the way God requires his people to deal with a person described as a fool, and as I already pointed out, a fool denies God in his heart, although His conscience bears witness. In verse 4, God forbids us from answering a fool, (Answer not a fool). In verse 5, God commands us to answer a fool (Answer a fool...).
Why this seemingly contradiction? Because of the reasons attached to the respective phrases. The rest of Scripture will show that the decision to answer or not to answer is not arbitrary. A person’s (the fool) character/attitude, circumstances and time are some of the factors used to determine if to answer or not to answer. In verse 4, the reason is so that you will not be like him in his foolishness. You are found arguing with a fool and possibly, it may not appear as if there is a difference between you two! This is what King Hezekiah told his people to do - not to answer Rabshakeh who was mocking and spitting blasphemy against the true and living God and his people (2Kings 18:36).
If you must respond, then it definitely must not be according to the fool's foolishness. This is what the Apostle Peter said, 'Do not repay evil for evil or reviling for reviling, but on the contrary, bless for to this you were called, that you may obtain a blessing.' 1(Pet 3:9). Effort is needed to restrain oneself from responding to a provocation, cynical or sarcastic questions. The Lord Himself, when faced by the Sanhedrin who were challenging His authority, declined from providing them with answers to their questions. Instead He asked them one question and demanded an answer as an cue for His providing them an answer. But when they refused to truthfully, sincerely and honestly answer His question, He told them that He was not going to answer their question (Mark 11:27-33).
On the others hand, there are times and circumstances when you have to respond, obviously not unwisely, but wisely with words seasoned with grace so as to make them edify the hearings, like I am doing. I draw example here from the Scriptures from such men like Job. Job responded to his wife, "You speak as one of the foolish women would speak. Shall we receive good from God, and shall we not receive evil?" (Job 2:10) Job had to expose both the wife's foolishness – “…you speak as one of the foolish women...” but he also went to on spell out for her the need for them to embrace providences of God – “Shall we receive good from the Lord and not evil?” Again you notice that Job has argued by folly – to show that she was being as other foolish women but also by truth, presenting truth on the providence of God.
In conclusion, there is a place for a response even to those in blasphemy, but also room for refusing to respond. Either way, there has to be a resolve not to be like the fool, retorting in a manner that shows you are as good as the fool. Moses' response to the rebelling crowd at Meribah is a good example (Numbers 20:2-9) for this foolishness Moses was disciplined by God and did not get to the promised land.
Therefore a response is to be given with the resolve to help the fool from his folly. He must not remain conceited thinking that he is the wisest man ever lived when wallowing in his foolish ways, 'lest he be wise in his own conceit'. You want him to be brought from folly and pride and so you speak to help him see these sins.
Please bear in mind that foolishness is as much a sin as anything else - Mark 7:22, Titus 3:9 etc. and will deliver those who glory in it to hell. If you reject truth, and mock truth, and malign truth, you are a fool, for you live a lie. However, there is hope for you in Christ, the wisdom of God:
For since, in the wisdom of God, the world did not know God through wisdom, it pleased God through the folly of what we preach to save those who believe. For Jews demand signs and Greeks seek wisdom, but we preach Christ crucified, a stumbling block to Jews and folly to Gentiles, but to those who are called, both Jews and Greeks, Christ the power of God and the wisdom of God. 1Corinthians 1:21-24.