Armstrong had decided on this statement following a train of thought that he had had after launch and during the hours after landing. The broadcast did not have the “a” before “man”, rendering the phrase a contradiction (as man in such use is synonymous with mankind). NASA and Armstrong insisted for years that static had obscured the “a”, with Armstrong stating he would never make such a mistake, but after repeated listenings to recordings, Armstrong admitted he must have dropped the “a”.  Armstrong later said he “would hope that history would grant me leeway for dropping the syllable and understand that it was certainly intended, even if it was not said – although it might actually have been”.
One of the most weirdly riveting Wikipedia paragraphs I’ve ever read