A person who changes their mind after better evidence did not lose; they upgraded.

Changing your mind when the evidence changes is the system working, not a defeat. It gets treated as a loss because of how disagreements are staged, as though a position were territory. In terms of what you actually have, you now hold a more accurate view than you did, which is straightforwardly better.

When you find yourself resisting a good argument, notice whether you are defending the position or your standing. Then say plainly that you have updated, and say why. Doing it openly a few times makes it much easier, and it tends to raise rather than lower how seriously people take you.