Where I am over here in Southern France things seem to be a bit different.
At a beginner level there is an equal number of boys and girls riding. As the years go by however the boys seem to vanish, if you randomly pick 30 novice riders there will be maybe 3 or 4 boys. When the level goes up though, nearly all the girls "drop out", they have no wish to progress further than walk, trot, canter and jumps up to about 70cm. The boys often don't quit though, they mostly want to improve further than being weekend riders. The result is a small group of riders where 1/3 is a boy, by this level, progression can only be achieved by buying a horse and going to a competitive level. At "amateur" level (the first money earning competition level in France) the male 1/3 is very apparent. The girls once again mostly drop out though before "pro" level (pro riders are expected to have an entire show barn of 50k horses they trained from scratch by most people), I have yet to meet a woman training and competing at pro level.
Conclusion: There are plenty of men who ride, just not many who own horses outside of top level competition.
In my opinion it is because around here men have an attitude of "look at me, look how strong I am, I can hold this poor defenseless horse in rolkur, because I am a man and I ride big horses"
(fun fact: most men around here own mares and there are virtually no geldings in the area, at any level)