I do think boys/men seem less likely to keep up/take up the sport as leisure riders. I have known riding schools where a number of boys had lessons- I think having a critical mass of boys and older boys present helped as it gives the younger boys role models to look up to, and they don't see it as just a girly thing.
However, one issue that boys can run into more easily is that it doesn't take being an abnormally large 16yo to outgrow many riding school weight limits, and finding a first horse as a 14st 16yo novice is a lot harder than doing it as a 10st novice 16yo girl- the horse for the boy is likely to be more expensive in all ways, and potentially a scarier prospect if the boy is a bit overhorsed.
Definitely in families with children who ride their own horses, the boys usually seem to ride too (although if only one child rides, it usually seems to be a girl!). I've known a few boys on yards who are involved in pony club, and at least one was already showjumping to a reasonable level at about 14.
One thing to bear in mind with showjumping is that at even at local level if you can go out and win a class then there's normally a half decent prize- maybe not cash, but certainly goodies and even tack shop vouchers etc, and sometimes enough cash to at least break even on your petrol- there's nothing like this in other disciplines, at least around here until you're getting to a pretty decent affiliated level. Perhaps this chance to win a tangible prize attracts boys more? Perhaps it's also seeing male role models in the sport?
Certainly, it is possible to make a reasonable living as a showjumper, even if you aren't winning big classes all the time. And there can be less options for men to make money in horses- I know a few young women who make a reasonable living schooling ponies, and backing children's ponies- if you're light enough to produce a decent 12.2hh or 13.2hh pony, then it's usually possible to make a reasonable profit. I think it's much harder to do this with a 15.2 or 16.2 unless you get a competition record with them- but I'm happy to be corrected!