He was being brave when he brought his problem to his superiors and said he'd like to quit. Actually, the only "braver" thing in this situation would be to quit anyway, without letting them "talk him out of quitting". But that could have been also stupid, we don't know the exact circumstances.
On a more general note: everyone should try to ~~contain~~ [edit: solve!] his/her ego-issues (and other psychological issues) as much as possible, of course. But placing someone with mentioned issues on the project which caused these issues in the first place is clearly a fail of management. If "soft skills" are so important (and they are), then the management should use them! Management should place employees in an optimal environment so that psychological issues are less likely to occur. Making people work for a long time on things they are averse to is a recipe for disaster. Both for the employee and the project.
I had to be talked out of quitting a couple of times. I think they might have been better letting me quit the first time, and getting a replacement who didn't have so much ego affecting their work.