Significance of the word 'a' in Neil Armstrong's speech [duplicate]

Possible Duplicate:
“That’s one small step for man, one giant leap for mankind.”

I read on the news today the world heard Neil Armstrong said "That's one small step for man, one giant leap for mankind.". But later, Neil Armstrong insisted that he actually said 'a man' but that the 'a' was not heard because of static. So this begs the question "What is the difference between the 2 versions?" Is the version that Neil Armstrong wanted the world to hear a grammatically correct one and the other one is not?

If you read the first 'man' to mean the broader humanity/mankind, the phrase sounds a little goofy:

That's one small step for mankind, one giant leap for mankind.

Huh? How can it be both a small step and a giant leap for mankind at the same time?

Whereas if you read it the way Armstrong allegedly meant to say it:

That's one small step for a man, one giant leap for mankind.

Now it makes a little more sense. It's just one guy taking a little step off a spaceship, but it represents a giant leap forward for mankind as a whole.

• For a man means for an adult male human.

• For man means for mankind in general: for all humans.

So to skip the a reduces the pronouncement to some sort of nonsense, since now they are the same thing.