Greetings. Once I realized that the conversation has gotten into another leg, I will simply stop saying a thing, I do not like arguing as well, if keeping shut will make the person win, so be it.
But it's true with what you said, when a party that was involved in the argument keep shut, it does not really mean he has admit that he/she was wrong, so if I want to let someone know a thing, I do not go through argument, as it does not help.
Wise words, comrade. Better to find common ground and have a connection rather than build resentment