I was an instructor in the military for a few years and taught a course on leadership. We covered the "Great Man" theory in one of our classes, and the main argument against it is the theory ascribes to the belief that "leaders aren't made; they're born." This runs contrary to what we are currently trying to teach in the service. We have gone away from this type of model, at least in my branch, because we want to develop leaders. Telling someone you are or aren't a leader based on how you were born isn't very conducive when you're trying to teach them that everyone can be a leader.

Many other theories have popped up since then that give a person the opportunity to recognize and develop their leadership skills. The one we teach now is Full Range Leadership Development (FRLD) that has four specific things you can work on. This encourages people to be transformational leaders based on their inspirational motivation (charisma), idealized influence (character), idealized consideration (caring), and intelectual stimulation (intelligence). This theory is based on many previous leadership theories--the "Great Man" theory being one of them.

A theory like FRLD is more popular because people are allowed to work on themselves rather than being told you are never going to be a leader because you weren't born one a leader. Again this if from my perspective teaching this in the military so I'd expect there to be differences in the civilian sector.