So Moshe Rabbeinu tries to get Hashem to choose anybody but him. What's his problem? It's really very simple and it goes to the heart of the true essence of humility and humbleness. Moshe was not an am haaretz - an ignoramus. His sister and mother, throughout their caring for his childhood while in the court of Pharoah, taught him Torah and Kabbalah (Remember Shifra and Puah? They were his mother and sister). When he smote the Egyptian taskmaster, it was not by the force of arms but rather through the kabbalistic manipulation of Hashem's Ineffable Name.
Moshe Rabbeinu had a healthy self-image. He just didn't want power. True power is in Hashem's hands. When man assumes power, well, power corrupts and corrupts absolutely. Hashem chose Moshe precisely because Moshe didn't want the power. We find this same theme in Jonah's story (a whale of a guy). It is only those that have no need, use or desire for power that Hashem can trust to be a vehicle for His power.
To quote Reb Shlomo Carlebach, zt"l from an interview in Gnosis Magazine in 1990: "Remember the difference between G-d building bridges and government building bridges? The government builds bridges with people who know how to do it. G-d builds bridges with people who are desperate that the bridges should exist! I don't know how to do it. But I do know that I am desperate-that it has to happen."
Addendum: Pharoah in Hebrew is spelt 'peh', 'resh', 'ayin', 'heh', which also spells 'peh rah' - evil mouth. My name is Moshe Pesach, and I obviously am karmically connected to this part of the Torah. Pesach is the pascal sacrificial lamb. Pesach is spelt 'peh', 'samech', 'chet'. which also spells 'peh sach' - meaning mouth that speaks. The fixing of the evil Egyptian kings' mouth is Moshe's pure mouth.