Not a native speaker, but my guess is that "Women don't like him" would be translated as "Frauen mögen ihn nicht."
This is confusing but idk how to describe why. It's talking about multiple women but does not use Frauen??
You could phrase it 2 ways in English: "No woman likes him" and "no women like him". I think you could say both in German as well: "Keine Frau mag ihn" and "Keine Frauen mögen ihn".
Just like in English. It's acutally not talking about multiple women. It's talking about zero women.
You disproved your own point by using the plural form "women" when you said "zero women".
Actually, they are right. You could say, "No house is big enough for me." Basically meaning that not a single house is big enough for me. "No man can swim across the ocean" is another example.
I wrote "no lady likes him" seeing in english woman and lady are the same thing but this site marks this wrong.