I have worked to be as rational as I will personally tolerate, and it has been difficult, but I've achieved some success. The key is to divorce your identity from your beliefs about the world, and to realize that the opposite of never admitting you're wrong is "always being right", which is of course impossible, so if you are TRULY interested in becoming MORE right, then the only reasonable option is that you must sometimes lose arguments (and admit it to both of you).
Are most people interested in doing this? No, and in that sense you have a point. But it's available to everyone, and who wouldn't want to be more right?
The other difficult thing to do is to aim this at yourself with full candor and work through that. Interestingly, now that ChatGPT has access to all the conversations you've had with it, and assuming you've opened up to it a bit, you can ask it: "You know me pretty well. Please point out my personal hypocrisies." If you want to make it more fun, you can add "... as Dennis Leary/Bill Burr" etc. What it said when I tried this was fascinating and insightful. But also difficult to read...