Winning a point can delay solving the problem.

You can be entirely right, demonstrate it thoroughly, and be further from a solution than when you started. The other person is now defending themselves rather than working with you, and the problem sits exactly where it was while the score has been settled.

Ask what you want more: to be acknowledged, or for this to be fixed. If it is the second, let some winnable points go unmade. It is genuinely irritating and it is usually the fastest route to the outcome.