I have always liked the saying "sometimes you can be right, or get what you want, but not both". I've thought about it or repeated it to others as advice throughout my life, and have thus realized how many times it applies.

You're right. There are many many times when even then humblest hint that you are right will have negative interpersonal implications, which does make it hard to change minds.

I've also seen several times where I make a suggestion, humbly accept its rejection, and then, lo, a week later the other person has the same idea I suggested.