You're not right all the time
Your ego is the source of a lot of conflict and disagreement because it wants you to be right, making other people wrong.
Letting go of your need to be right is very powerful, even letting people win, even when you know are wrong.
is it a big issue? Will it matter in 5 mins?
No, then back down and move on. Flex your humility and your ego will no longer block your growth.