Gemara: What are examples of contradictions within Mishlei? It says, Do not answer a fool according to his folly" (Mishlei 26:4) and it says, "Answer a fool according to his folly" (ibid. 5). It is not a problem, as one is talking about matters of Torah (one answers) and one is talking about general matters (one does not answer).

Ein Ayah: People can make mistakes in judgment either because of intellectual shortcomings or due to problematic desires. Indeed many times people stray from the truth because their intellect confuses them. Some people diverge from the truth because their desires push them in the direction of mistake. In other words, if they adopt the mistake, they will be able to follow a path for which they have a desire. Instead of the decision remaining a matter of desire, it becomes entrenched in them as a matter of the intellect.
Mistakes of the first type (the intellectual) can be rectified by clarifying the matter based on intellect. Since the mistaken person only has a mistake of perception and he does not acquire the mistake as part of his nature, when he hears arguments that clarify the matter, he can leave behind his folly and embrace the truth.
The situation is very different for one whose departure from the truth is based on desires that have gone as far as to lead him on a path of lack of control and throwing off the yoke of Torah and ethics. Logical arguments will not have the desired effect on him because he will feel in his soul that if he embraces the path of truth that is contrary to his inclinations and wayward lifestyle to which he has become fully accustomed, he will turn out to be totally wrong.
The gemara gives these two paths to mistakes broad names that represent their dichotomy. The intellectual mistakes are called matters of Torah because the Torah’s purpose is to make one have the understanding of the ways of Hashem and His truths. It is true that mistakes of the intellect often cause one to stray in matters that are not under the heading of Torah per se. However, the basic foundation of the problem is under the category of Torah and decisions about ethics, belief, and wisdom.
The mistakes that are based on desires are called general matters because the inclinations that are likely to cause these desires are on matters that are connected to the body and not the intellect. It is true that eventually these desires affect and cause great damage in classic areas of Torah and the foundations of the holy religion. However, it is still called general matters because that is the root of the problem. Therefore, in these desire-based problems, the pasuk says to not answer the fool because it is not an intellectual mistake that he will fix when confronted with reason. Rather, it is something at the base of his evil heart that takes him to spiritually desolate places. Such fools can only be impacted by afflictions which subdue his haughty spirit (see Mishlei 19:29). These afflictions can remove the ashes of imagination from his eyes and let him see the corruption of his inclinations and the falsehood of his approach. For such people, speech is not worthwhile.
The above explains the difference between words of Torah and general matters.