Actually, I strongly believe there is a wrong stereotype in place which is why you get catwoman as a character whereas the term 'bitch' is derogatory.
Women are actually far more canine-aurad than feline-aurad. Men are the inverse.
I want you to observe wild cats to lion and tiger level and then observe wolves. After that drag down your observation to the domestic but base it more on the wild/feral forms of them.
Then list out traits of femininity and masculinity.
Why older women usually prefer cats and older men usually prefer dogs is linked to that most are hetero. I am not implying anything dirty, I am saying its about personalities they find more appealing.
Women like men that have their shit together that arent entirely submissive, generally. Is a pet cat or pet dog more like that? Men like an overall obedient partner that enjoys their dominance and leadership.
We can deny it, constantly. It is also more than the submissiveness aspect. Dogs are more emotional than cats. You can yourself look at traits of canines vs felines and you would realise we stereotype wrong. Women are not catlike.