As a guy in his 50s who has always liked horses but only recently started riding them, I think you've missed it. Here are my ideas:
1 - Riding horses is a girls sport.
No reason why it has to be this way, but where I live, you either are around horses because you live on a ranch and then guys will ride horses, or you don't live on a ranch and it is something for girls. At a riding stable around here, you would rarely see an adult male riding. Lessons are given by women. Drive by a stable, and you'll see 14 year old girls riding. No men.
Of course, this had to start somewhere. Being old, I remember that in the 50s and 60s, men worked and women frequently did not. I spent most of my life working 12+ hour days, and fully understand why most men didn't come home and drive to a stable and ride horses. But with no role models, riding became a woman's sport, or more frequently a girls sport.
2 - Relationships. Long term training with a horse is a relationship. Most guys are goal oriented - do something to win something. You don't train a horse to win much in a year or two. In fact, you don't train them for much of anything unless you first spend some years learning yourself.
A guy looks at it and says, "A motorcycle doesn't need attention, I can learn to ride myself, and I can buy a moderately competitive cycle at a price I can afford.
Mia believes her real title is "Queen of the Universe", but in reality, she's a decent mare who was used for about a year for endurance racing by a guy, who then decided he needed something better. So she wasn't ridden for a year, and then was donated to a charity.
I bought her on a whim, started riding because I had just retired and was bored, didn't think much of it and was surprised a year or more later to discover that I liked her, and she liked me. I'm learning to ride by reading books and by climbing on her and seeing how she responds to different things. But it never occurred to me at the start that a horse would also end up being a friend...
Females are more relation based, and on average more likely to do something because of the relation it builds. That works well with riding a horse, particularly when you understand that the "Queen of the Universe" will never actually win anything.
For most guys, a motorcycle is faster, easier to learn, cheaper to own, goes more places, and you don't have to worry if the motorcycle likes you or respects you.
Anyways, those are my guesses. It is a pity. IMHO, riding horses is far more 'macho' than riding a motorcycle, and besides, I get tired of seeing questions posted on forums like "Is this horsie name cute enough?" and "Does this saddle make my butt look big?"
BTW - the braids were done by my wife. The photo is over a year old, and I have since trimmed Mia's mane to make it easier to brush and go...