You can be right about the facts and wrong about the person.

Winning the detail and losing the person happen together more often than people expect. You can have the date, the number and the wording exactly right and still have misread what somebody meant, what they were worried about, or why it mattered to them at all. Being factually right feels like being right about everything. It is a much narrower claim than that.

In your next disagreement, work out what the other person is actually upset about before proving your point. Say that part back to them first. The facts will still be there afterward.