RE: Proving that you are right is just a necessity of your brain!
You are quite right about the psychological part.
However, I've found out for myself that there are things worth arguing about, even though I know that the other person will not accept any of my arguments.
I normally will concede in the end: "Alright you have your opinion, and I have mine."
And we leave the scene without any winner or loser.
But I know, if my arguments have actually be solid, they've planted a seed that might grow roots in the future, even while at the present accepting the arguments would be far too painful.
Sometimes that future is already the next day, particularly when I have argued with my kids. And sometimes the future is after ten years or longer, if the person I argued with is no longer a kid and his or her psyche is much larger.
And sometimes the future comes for me after the other person has planted seeds that have grown to fruition a long time later, seeds my fragile psyche needed a really long time to allow them to grow.
Even if your arguments are solid are just in your head, because in other person's head are not that solid. It all depends on how you take them and accept them. I like your opinion about everything and if you think that's the right decision for you then you should do like you think is best no matter what other people says.