Moshe Rabbeinu led Bnei Yisrael for approximately 41 years. In our parasha we find him seeming to cave in under pressure. "Did I conceive this nation or did I give birth to it, that You should say to me, ‘Carry it in your bosom as a nursing woman carries the nursing baby’ .... I will not be able to bear this whole nation alone, for it is too heavy for me" (Bamidbar 11: 12, 14). What caused the shaking of Moshe’s resolve? After all, he had weathered worse storms, such as the danger at Yam Suf, the Golden Calf, etc. He would continue in his post for another 39 years and act strongly in such events as the spies and the rebellion of Korach.
Let us take a look at what "set off" Moshe. The people complained that they lacked meat, even though they had an ample supply of manna. On one hand, the stakes were lower compared to some of the other episodes where Moshe showed strong leadership. However, this may have been the problem. Moshe rose to the occasion to fight for real issues: to save the lives of the people, to fight idolatry and defection from Hashem’s plan for the nation, etc. In this case, the matter was just dealing with human frailties, i.e., the desire for meat instead of manna. The man of G-d found it hard to deal with the disrespectful "kvetching" of people on such a mundane matter.
This idea may explain the analogy Moshe picked. A nursing mother wants nothing more than to feed her child. Yet sometimes the baby feels hungry and becomes impatient with his mother. A whimper would suffice to bring the mother to fulfill his desires, but instead he may cry inconsolably for what he wants, until he is not even able to enjoy it when his mother is ready. It is a rebellion without a cause. A baby does it in one way; a nation, including Bnei Yisrael, will have a more sophisticated type of tantrum. This was a human frailty that Moshe had trouble dealing with.
It is interesting how Hashem answered Moshe. As Moshe did not want to continue alone, Hashem had him find 70 people who were "elders of the nation and its task masters" (ibid.:16). Rashi points out that these were men who received lashes instead of Bnei Yisrael when the latter were unable to finish the unreasonable work Pharaoh had decreed upon them. They had given of themselves for the people in a matter that showed sensitivity to their brethren’s pain. Why should they get hit, especially when some of Jews probably did not pull their weight to the maximum? They were simply people who were sensitive to the suffering of others who lacked the backbone to absorb difficulties as they did. While Moshe also showed his sensitivity, he needed partners in this regard.
Leadership requires more than heroic acts and visionary shepherding. There is also a need for those who understand the way the simple person feels and are willing to deal with the pain that accompanies human frailty.