Many Unmarried Men are not Bachelors
In philosophy, the sentence "all bachelors are unmarried men" is often used as an example of an analytic truth. "Bachelor," so the story goes, just means "unmarried man."
But, now that I think about it, this is not what the word normally means. All bachelors are unmarried men, but the reverse is not true. The Pope is definitely not a bachelor, neither is a Buddhist monk. A thoroughly asexual guy is only sort of a bachelor. The word means something more like "a man who is not married but might want to be."