As a fourth grade teacher, I have a certain degree of patience (that is very little) for bad grammar and usage. I have a standing threat for the kids in my room that says that I will swat them in the back of the head if they use an apostrophe in a plural. So far, the threat has been sufficient, but there's still an element of danger in written language for my students.
So how would I feel if one of them grew up to be the first person to set foot on Mars, and they said, "That's one small step for man, one giant leap for mankind?" I want to believe that I would be so impressed with the accomplishment that the missing article ("a man") wouldn't be my initial concern. But over time - seeing it on coffee mugs, plaques, t-shirts, and hearing the tape loop played endlessly - it might start to grate on me that one of my students was clever enough to manage interplanetary travel, but not practiced enough to come up with the proper grammar to announce the momentous occasion.
Imagine how relieved Neil Armstrong must feel, thirty-seven years after the fact, to find that poor recording techniques may be to blame for his omission at Tranquility Base. In a graphical representation of the famous phrase, computer programmer Peter Shann Ford said he found evidence that the missing "a" was spoken and transmitted to NASA. Imagine the relief he must feel, knowing that he no longer has to wait in fear of his fourth grade teacher sneaking up on him and whacking him in the head.