Why did Moshe not want to go on the mission to free the Jewish people from Egypt? Was he just being modest? Or, did he not want to be the leader of the Jewish people?
The answer is that Moshe was atypical of leaders of nations. Leaders are self-motivated to become leaders. This drive comes about due to their ego or because of their belief in their particular cause. Moshe initially did not have this self-motivation, but why did he not respond more positively to G-d’s request? Was it just his sense of humility? Why was he not concerned about the fate of the Jewish people? Also, one would also have thought that the honor of being chosen by G-d and the opportunity to be G-d’s messenger would be enough of a reason to accept the mission. Yet, Moshe clearly did not want to go on the mission. Here goes for some speculation for why Moshe did not initially accept G-d’s request for him to take the Jewish people out of Egypt.
One possibility is that initially Moshe did not fully comprehend G-d’s power, and he might have thought that the mission would fail, as he stated after his first encounter with Pharaoh, 5:22,23. Also, afterwards G-d told Moshe that the people who were seeking his life were dead, 4:19, which indicates that Moshe was worried that he could die from the mission, though maybe this was just an excuse for Moshe. With this approach, the miracles of the burning bush (3:2) and the three signs (4:2-9) were not enough to convince him of G-d's powers. Could this be?
A second possibility is that Moshe's hesitancy was due to his feelings for the Egyptian royal family, if not to Pharaoh. We see from the reason for the name of Moshe’s son, Gershom, that Moshe thought of Egypt as being his home, 2:22. With this approach, Moshe would have realized that taking the Jewish people out of Egypt would have meant using force against Egypt (3:20), and maybe he did not want to destroy the people and the home where he had grown up.
Also, with this approach, Moshe was not sure of his ultimate loyalty: To the Jewish people or to the Egyptian royal family? I once suggested this in a class, and my daughter Talia and Annie Rosen suggested, that maybe because of this problem, G-d responded that Aharon your brother was coming to meet you, 4:14, to stress that his true identity was with the Jewish people, his family. In addition, the actions of the Jewish taskmasters who yelled at Moshe (and Aharon, 5:20,21) might have helped sway Moshe to identify with the Jewish people and not the Egyptians.
A third possibility is that while Moshe did not have much feelings for the Egyptian royal court he also did not have enough feelings for the Jewish people. All decisions are based on cost/ benefit analysis and maybe Moshe thought that the cost of the mission was greater than the benefits. The costs were a huge amount of work, separation from his family for a long period of time, and possibly the loss of a comfortable life in Midyan. The benefits would be the feeling that he helped save the Jewish people from slavery. However, that feeling would only be powerful enough to overcome the costs involved if Moshe felt a strong connection with the Jewish people. Did Moshe initially have this strong emotional bond? Maybe not. Moshe had been raised separate from the Jewish people and had lived outside of Egypt for many years. Also, maybe his bad encounter with the two Jewish men fighting, 2:13,14, soured him on his feelings towards the Jewish people. Therefore, for Moshe to want to be the leader of the Jewish people it was necessary for him to develop an emotional attachment to the Jewish people, and this is what occurred in chapter five through the intentional failure of his first mission to Pharaoh and the criticism by the taskmasters.