Being right isn't enough: we have to be right at the right time. If the time isn't right you will lose a lot more than just the argument: respect, authority, good will, support, possibly even trust. All those things take a long time to build and it's a very high cost to pay for being right and ignored.
Experience is also knowing when to step back without giving up. it's knowing how to avoid getting angry because "What starts in anger ends in shame" (Benjamin Franklin)
And remember, your relationship with them is worth more than being right, so drop it. For now. The time isn't quite right yet.