Why won't people just accept the fact that EVERY single one of us probably has something that we are completely inflexible about? If a SO won't accept something and has their feet firmly planted, trying to discuss that something with them or compromise or convince them to change their beliefs is likely only going to make things worse.
It doesn't matter how long you beat a dead horse. He is still never going to get up and all you are going to do is wear YOURself out.
