My point, which you seem to have missed, is that N people can claim to be great "if only X wasn't in my way". In reality, an infinitesimally small number of people will be judged as great by history, and half of those will be largely by accident, many will not realize it, and some will only achieve it post-mortem.
Therefore, logically, if someone claims to be great, they are mostly likely riding high on hubris and ego. It's statistically the most likely outcome for anyone claiming greatness.
Because that wasn't your point. You claimed it's hubris and ego because greatness is in the eye of the third-party beholder. Now you argue it is necessary that greatness must be unlikely, which is of course true but changes nothing. History of science, maybe history of progress is the history of (at that moment) unlikeliness prevailing.
Therefore, logically, if someone claims to be great, they are mostly likely riding high on hubris and ego. It's statistically the most likely outcome for anyone claiming greatness.