At the Guinness brewery, they had a human-sized animatronics fish riding a bicycle, I bought a poster with a cartoon of it when I went. It must be a more common saying in Ireland, it was also in a U2 song.

Ya’ll realize this is just saying a woman doesn’t need a man? Like, a man also doesn’t need a woman, or a fish a bicycle. Doesn’t mean men as a whole aren’t important or don’t do important things that society needs. It’s just that a woman isn’t lacking if she’s without one (visa versa for the fellas).