Why do we say a dog is man's best friend and diamonds are a woman's best friend?
The equivocation here has already been noted by others. It occurs when a word has two or more distinct meaning that are used interchangeably (I call that two words, the dictionary calls them homonyms, but that's a fine point). The example I like to use when discussing this topic, which usually comes up when somebody conflates two different meanings of the word faith, uses bank (a place to keep money) and bank (the shore of a river). An equivocation fallacy might be, banks are a safe place to keep money, rivers have banks, therefore rivers are a safe place to keep money.
"Man" and "a man" are different usages. "Man", without an article, generally denotes mankind, rather than men as opposed to women.
Neil forgot that article, and it makes a difference, although it is one nobody notices: "That's one small step for man, one giant leap for mankind." Without it, the statement essential says that that was both one small step and one giant leap for mankind, which is obviously not what he meant.
For a while, people in Scunthorpe couldn't use AOL services, because the profanity filters deleted their addresses.
I knew somebody who went to Beaver College. She couldn't search her college on campus because of those filters.