I need to learn a similar lesson. My team lead isn't used to being questioned, and when I tried to correct him in a meeting it resulted in a big argument. I realized that I did so partly because I wanted to demonstrate my own knowledge. We were both being egotistical. Certainly he could have handled it better, but I could have avoided the problem entirely by finding a more tactful framing rather than correcting him publicly.

I guess the generalized version is "it's easier to get what you want through compromise and avoiding conflict." Or just, "you catch more flies with honey than vinegar."