I know what you mean AstroChuck. But only Western society seems to do that. In other cultures (e.g., Asian cultures) dogs and cats have no gender class. It’s mostly culture specific.
My guess is that dogs have always been associated with hunting (they are pack animals), and because men were traditionally the hunters, dogs became associated with them instead of being at home with the women. Cats are more recent domesticated animals than dogs, and their role was always close to home and hence the women. Dogs are also loyal animals that take to a leader in the pack, and since men have traditionally ruled the household. they respond to their male masters, hence the connection. Thirdly, dogs are on the whole rough and tumble sort of creatures, desiring of physical activities, unlike cats. Because men engage in sports and outdoor physical activities more than women, dogs have always been their constant companions and playmates. Cats are creatures of comfort, and because in this society women are socialized by the media to seek comforts like fashion, jewelry, tending to the home, etc., they traditionally have associated with cats more. Cats also are “softer”, more graceful creatures than dogs, generally, stereotyped characteristics that are associated with the female sex. And it doesn’t help when Hollywood comes out with silly movies like “The Truth About Cats and Dogs”. Lol.
Personally, I love both dogs and cats, and have never associated either animal as more “male” or “female” based. I’ve owned both cats and dogs in my life, and some cats, (eg., tomcats are very masculine with their bold behaviors and square jowls), give some dogs a run for their money. Lol.