One of the things Cool Hand Luke made me think about was the way we treat celebrities, and the reasons for this.
The prisoners, finding that Luke is beyond intimidation, treat him with great favour, building to something like hero worship as the film goes on. When he is finally broken by the prison authorities, the other prisoners turn away from him in disgust. This phenomenon is well worth trying to understand, as it is something that we are all naturally prone to, I think, and can be very dangerous.
Psychologists (some of them, anyway) like to talk about the 'ideal self' - where there is a disparity between my perceived self and my ideal self, we are troubled by the resulting cognitive dissonance. The phenomenon exemplified in Cool Hand Luke seems, to me, to suggest the existence of a converse self (I am stuck for an opposite to 'ideal') - the self that we secretly fear ourselves to be. For many people, this self is craven, easily cowed, nothing special, unattractive, foolish, etc. I believe that the struggle towards the ideal self may be just as truly the struggle away from this worst-case, gollum self.
With this in mind, we can see that Luke's indefatigability challenges many inmates' perceptions of themselves, forcing them to re-examine their position in relation to their best and worst selves. Luke doesn't bow down to anyone, not to me, nor to those to whom I bow down. If I'm not Luke, who am I?
The inmates' coping strategies all demand that Luke be so great that they could never be expected to be as good as him. If Luke is just a guy, good but not great, then why aren't I like him? But if he is a hero, a man who can eat fifty eggs, a man who will never quit, then there's nothing wrong with not being him - for who could be?
All of the hero worship that ensues, as fun as it seems, is never going to end happily. Inevitably, when Luke is incontrovertibly shown to be a mortal man, an attainable goal, the prisoners are left with no choice but to put him right down instead, as not worth imitating in the first place.
All of which is pretty unfair on Luke, just as it was unfair on Jesus, and Kurt Cobain, and all the others we've done it to over the years. Some, like mainstream musicians or actors, rely on this tendency to make them famous in the first place; they can't complain, really. But when we do it to those who are truly special, we do them a disservice.