It’s not that cat ladies are weird. It’s that cats themselves are strange creatures and this bias intensifies the weirdness of the owner.
Cats don’t get out of the house, generally. They’re individualistic, pre-trained, and too smart for their own good. They act like they don’t need humans.
Cats purr and show love. They too have hearts. But cats get relegated to the odd echelon of domesticated animals. And their owners take on the same stigma.
Dogs aren’t saints either, but their outgoing behavior makes them appear more sociable and therefore more likeable. Dogs act like they care more, with tongues that give licks of joy. But dogs require more human control.
Dog owners make the dog. The cat makes its own journey. Perhaps its the human that works for the cat.