Friend Zone is the concept that once you fail to push the sexual advance upon a woman she will regard you as merely 'a friend', or as an emotional support device. She will date more assertive/aggressive men while you will be the person to talks about these men (and their failings) to.
Wait... that sounds reasonable. Why is this concept controversial?
There is certainly a difference I feel between people who come onto me as a friend versus people who come onto me sexually (though all the people I ever got a crush on have TYPICALLY been not as aggressive... with only two of my five crushes in my entire life have been with people who ever actually come onto me)
I mean I know how this concept could be misapplied, but at surface value it simply means "If you speak to someone as a friend they will regard you as a friend and might not immediately see you as a romantic interest"
Because the whole thing is sexist, that's why. If you want to date someone and they want to be friends with you, you haven't been "Friendzoned",
you've been turned down. No one owes you sex.
Stereotypically, the people who use that word will befriend a woman with the aim of having sex with her, and then when they get rejected they get angry because they did so much for that person. But him being rewarded with sex/romance was never what was in question, she just saw it as a friendship.
Basically, it "doesn't exist" in the sense that its a dumb concept that should be erased from our language, not in the sense that there can't be a relationship in which one person wants friendship and one person wants romance.
Also,
obligatory XKCD.