I can think of a lot of good reasons for both arguments, and the Soviets made the opposite call for their lander, but what I'm interested in here is this:

Given the mass penalty of another man (body weight, supplies, oxygen, propellant) and given the LM's extreme optimization for mass, why did NASA decide that two astronauts needed to land on the moon instead of one?

Obviously this decision was made very early on in the LM's development. NASA must have known what a weight penalty this would impose, and what a crunch this would put on the rest of the vehicle. Was there just not enough confidence with the guidance systems at that time? Was there a strong sense of "you're going to need a buddy system for this to be safe"? Of course, it ended up being the right decision, as Buzz Aldrin came through during the LM's descent for Apollo 11.