The quiet after an argument is where you find out if you were right or just loud.

During an argument there is no room to evaluate anything, because you are busy holding a position and watching for the next opening. Afterward, with nobody listening and nothing to defend, the real quality of your case becomes visible. Sometimes it holds up fine. Fairly often what felt like conviction turns out to have been volume, momentum, or not wanting to lose in front of somebody.

An hour after the next one, run your own argument again with no one there. If it still stands, say so calmly later. If it does not, admitting that costs less than you expect.