That's why when a person is upset and has a hard time expressing themselves, or when an old person struggles to explain the importance of some traditional custom to a new generation, people tend to automatically dismiss them. We often care more about winning arguments than about finding truth.
You contradict this later by saying "We often care more about winning arguments than about finding truth." This is right - it's not that people think that winning the argument means they're correct, it's just that it feels good to win an argument. Winning does matter more than finding the true. Why? Feelings. Feelings govern everything. Life would literally have no meaning without the feeling tones that give it meaning.
We should also resist the temptation of declaring victory in a discussion and instead listen carefully to what irrational, emotional, even inarticulate people have to say.