I thought Buzz piloted the lander and Neil was the mission commander? I'm still in the middle of listening to his biography, _First Man_, but they chose Neil to go up before they even took off, because they felt Neil was more level-headed than Buzz, and would handle the fame and attention better. Of course, they couldn't tell the public this. What they said was that it would be too hard for the pilot to reach the door with his suit on and Neil in the way.
