A Gentle Answer

Proverbs is not full of exclusively universal truths.  Unlike the intrinsically necessary (and thus universal) truths of reason or the moral obligations of Yahweh in Mosaic Law, its descriptions of how people behave are individualistic, bound to specific situational contexts.  The claims of Proverbs 15:1 could not be true otherwise: "A gentle answer turns away wrath, but a harsh word stirs up anger."  People could have various personalities or, though there is no excuse for anything short of metaphysical/epistemological rationalism, conflicting worldviews that will lead them to react from person to person in differing ways to the same scenarios.

With Proverbs 15:1, one can realize that there is more than one logically possible outcome when using gentle or harsh words simply because it does not follow that, say, a kind statement will necessarily lead to a pleasant exchange.  What some people perceive as harsh might not be harsh in vocabulary or intended meaning at all, but this aside, harsh words do not inherently trigger a hostile conversation.  The aggressive speaker could alter their attitude at any time and the other party decides how they respond no matter what it is they are reacting to.  A naturally calm or detached person could remain stoic or even actively kind even in the face of distinctively harsh words and tone.  Gentleness can be illusory anyway.

All of this is inevitably about logical truths, not what a book says or what someone's social experiences or hearsay from others have been like.  That is not to say that Proverbs is false.  It does not follow that Proverbs, which is addressing things that are consistent with logical axioms (and other strictly necessary truths) without misrepresenting them, is in error.  For example, Proverbs 26:4-5 says back to back to not respond to a fool in a like manner, lest you be like them, and to respond to a fool according to their folly, lest they think they are in the right.  Philosophical errors (assumptions or belief in contradictory things) and immoral/foolish behaviors cannot be valid, of course, so Proverbs is not prescribing either since the Bible is heavily moralistic.

In such passages as Proverbs 26:4-5, especially with the statements being directly next to each other, the verses are about more sarcastic or contextual truths.  Saying that a gentle answer turns away wrath is an amoral acknowledgement of what might (or might not) actually come about from using gentle words.  Maybe you will receive a calmer engagement from the other party, maybe not.  There is no guarantee that someone who initially sheds their aggression will not go right back to it even if they are the one who deserves hostility.  It is not as if gentleness is an automatic moral requirement according to the same book that contains Proverbs.  Anger and aggressiveness can also be perfectly valid when directed against stupidity and sin without stooping to them.

Besides the Torah's prescription of righteous deeds like limited flogging of some offenders (Deuteronomy 25:1-3, and see also Proverbs 26:3, which is consistent with the former while lacking a great deal of context on its own) or the killing of others (such as with Exodus 22:18-20), the New Testament itself is not about gentleness.  Among other things, Jesus says in Matthew 10:34 that he did not come to simply bring peace to the world.  Revelation 19 sees the returning Christ kill many people as well.  Yes, peace will be the final eschatological condition of the cosmos and the humans that still exist into eternity according to the Bible (Revelation 21:3-4), but that is after all of God's enemies have been permanently killed in hell (Matthew 10:28, Revelation 20:25).  Gentleness is not the same as rationality and moral goodness.