Most matters gridlocked by personal pride are cloaked as matters of "principle". They're not.
It seems like a matter of principle when you're mad as an angry bull and can only see the color red. "I can't let him get away with doing that to me," the attitude goes. "It's about the principle!"
Principles are important. Without them society breaks down entirely. So, look at the deeper principles truly at stake—much ado about little, mountains grown from ant hills, grown adults squabbling over matters so silly, children can't notice the difference. Being petty is also a matter of principle.