An internal argument can continue long after the real person has changed their mind.

You can be arguing with a version of someone who has moved on. The rebuttals continue in your head, the case gets refined, and the actual person changed their view months ago or has forgotten the whole exchange. The dispute is now entirely internal and has acquired its own momentum.

If a conversation keeps replaying, consider finding out where the other person actually stands. Often the answer ends it immediately. And if that is not possible, notice that continuing the argument costs you time and costs them nothing.