Truth is of central importance in philosophy as a discipline. In a sense it’s all we care about. Where some say “truth be damned,” we say “everything else be damned.
If I say “The bird is on the wire” and you say, of the same bird at the same time and place, “The bird is not on the wire,” these are not alternative facts from which we may freely choose. For a statement to refer to a fact, the statement has to be true, and these cannot both be true.
But when statements contradict each other, or are inconsistent with each other, they are not two alternative facts; one is true and the other is false.
The phrase “my truth” is often used to refer to claims whose truth is more accessible to me, or important to me, than it is to someone else. Fair enough, but if it is a truth, then it is the case, and suggesting that I possess that seems like an affectation. What I may possess and you may not is belief about or knowledge of the truth. I think we would find less need to torture the word “truth” if we paid more attention to the concepts of belief and knowledge.
If we care about the truth, we should instead respond to assertions by asking “How do you know?” or “What are your reasons?” It is a strong disciplinary norm in philosophy that we assume the other person has reasons for their beliefs. It’s not that we’re naïve; we know it’s always possible that a person is rationalizing or motivated by self-interest, or has been led along by the crowd or tribal loyalty, but if we started a conversation by assuming any of those things about our interlocutor, we would be assuming we have nothing to learn from them. The philosopher isn’t cynical enough to think we know that.