Growing up, my family had a cat and later also a dog. The cat later died and was followed by another cat. Eventually the dog died and after some time there were two cats in the house.
So, I'm quite used to being around both dogs and cats and while I've always enjoyed the company of our cats, I've never seen them on the same level as dogs.
To me, a cat can be a pet, but a dog can be a friend and a companion. If that's not what you want, there's nothing wrong with just a cat.
As for the reactions from women, I wonder if it can be a subconscious analysis about traditional gender roles. Something along the lines of "If he can't be the leader of a dog, how can he be the leader of a family". It's just a stray though, don't read too much into it, please ladies.
I'd also like to chime in with a good old comparison between cats and dogs.
A dog thinks: "Wow, these people feed me, entertain me and keep me warm and safe. They must be gods!"
A cat thinks: "Wow, these people feed me, entertain me and keep me warm and safe. I must be a god!"