Well, I went to the Snopes link, so I can't debate the fact that Neil 'intended' to say (a) man. But, I sure am glad he messed it up!
I'm somewhat of a linguist by trade or training, and I feel strongly that 1) it sounds much better without the "a," and 2) it IS grammatically and linguistically correct without it.
The problem comes with the general public's lack of command of the English language, and/or understanding of other languages. The French version of this exemplifies my point:
"Un petit pas pour l'homme, une grand saut pour l'humanite."
Although "humanite" is actually a colloquial form meaning humanity as opposed to the more formal "humaine" which is humankind or mankind, it shows that this would be a statement by an average man under the circumstances.
In French, to say (a) man would be 'un homme' with 'un' being the masculine article. But, a detective would not say that "he got his (a) man," he would say, "he got his man."
The Snopes article says that Man and Mankind have essentially the same meaning in English (or at least in America,) but this is just not necessarily true. Although it can and does have the same meaning at times, it is also used quite differently at others.
Man is just a word for the male of the species, as opposed to woman. In French that would be L'homme. (The man) One would not say "un L'homme" for A 'certain' man, just un homme. Likewise, one would not say un homme when he just means 'man.' And although this is inclusive, it is not the same as saying 'all mankind.'
As evidenced in the above French translation of Armstrong's quote, there are different words in almost all languages to distinguish between (the) man, as distinguished from other lifeforms, and ALL men (or mankind.)
I believe Armstrong was/is a very intelligent man and perhaps subconciously was choosing at the last moment what his mind knew to be the correct usage. Unfortunately after the fact, he was shamed into accepting what he thought everyone else would have expected him to say.
Either way... the better form is, in fact, "That's one small step for Man, one giant leap for Mankind."
Notice how the articles agree, but are cumbersome, if one says in French, "Un petit pas pour Un homme, une grand saut pour un humain." In fact, you would never use 'un' with humain (a humankind.) You would use LE (contracted) for L'humain or L'humanite, and therefore laws of article agreement and good writing style dictate that you would also use L'homme instead of Un homme.
The correct translation into English then would be:
Un petit pas pour l'homme (One small step for Man,)
Une grand saut pour l'humanite (One giant leap for Mankind.)
Armstrong may have been misquoted, thank God. But, if not, then he was wrong about being wrong. The way he said it (or it was heard) was correct.