His use of the telling phrase "going down in flames" to describe friends of his who have settled down to a more steady, regular life hints at another fact that he doesn't want to have to face. The panic he can't see himself as having experienced tells me that he can't ever admit that for him, freedom's just another word for a debilitating fear of failure. There are so many strips that have him screaming in a blind terror he never will admit to having felt when confronted with the trappings of maturity that it's sort of easy for everyone but him to see that he lacks faith in his ability to be a productive member of adult society.
This leads us to another thing he will not admit to owing to a fear of the ramifications. The fact that he acts like a repellent jerk to anyone who would prefer that he deny himself a pleasure means that he doesn't want to admit that he is not the axis around which this world rotates. Granted, his inability to admit that he too must give way to others is a shared blindspot but it seems the most annoying to me owing to his nauseating immaturity.
Finally, he just can't admit that people aren't going to like every stupid, self-serving decision he makes because he makes it. As a for-instance, he doesn't much like it that Lawrence sees right through him because he doesn't want to admit that he thinks of Connie not as a person but as a convenience. Doing that would make him the bad guy and he can't do that.