I translated it to Greek and then searched. Not a great source, but a source. https://www.lexilogia.gr/threads/t%CE%BF-%CF%88%CE%AC%CF%81%... "The saying goes «το ψάρι, το κοτόπουλο και η γυναίκα θέλουν χέρι», i.e. "you should use your hand for fish, chicken and women". It is usually used as a joke, in a familiar environment, in order to urge someone, usually a man, who is reluctant to use their hands to eat fish or chicken, and stick to using their knife and fork, because they are embarrassed to eat with their hands.

An attempt at a definition: "you can't eat fish and chicken unless you grab them with your hand, and you should also use your hands on (your) woman". It is a play with the phrase "βάζω χέρι", which means to grope, to feel up. Not very politically correct, I know :)"

I think this is more of a joke that has moved through a bunch of cultures. In Chile, when I started to use silverware on chicken, I was told(with a laugh) the only things they eat with their hands there is chicken and women.

Of course that excludes all the things they eat on bread.