I saw Jim Hansen, Neil's biographer, at Le Bourget.
Remember, back in january 1969, thought and lobbied to be the first to walk on the Moon.
His argument: spacewalkers were always the number two..in Gemini and also Apollo 9. So HE should be the FIRST MAN on the Moon....
Counter argument: the hatch opens in such a way only an astronaut on the left side, can exit the LM, that would be Neil.
Counter-counter argument: Bean told Hansen "once on the Moon, astronauts can very easily shift places as they haven't donned their PLSS yet"....

So why was it Neil?

Apparently, Kraft, Low, Gilruth and another head of NASA (I forgot who) got together and debated who between Neil and Buzz should be the first out? They thought of Lindbergh and asked who was the most Lindbergh-like of the two? The answer was obvious! Neil has no ego, is more humble.... and the rest is history.