Massive digression, but the history of sidesaddle is really interesting. It wasn't a thing at all originally - women rode astride in skirts. Then (I believe it was her) Catherine de Medici started slinging one leg over the pommel of her standard saddle and eventually it became a 'decency' thing.
Early side saddles were scary - they just had a sort of cup that your top leg sat in. Modern ones have a leaping head - it's hard to explain but basically it sits above the lower leg (the one in the stirrup) so you can brace against it rather than just balancing and hoping for the beat! The 'cup' bit has been replaced by a pommel which sits above the leaping head so you can squeeze the two between your thighs - it feels extremely secure. The downside is that if you have a fall you might well not be thrown clear (especially in a riding habit, although these are now aprons over jodhpurs rather than proper long skirts) and if you have a rotational fall (ie the horse flipping on top of you) there are two big sticky out bits handy to pierce any internal organs they may encounter. However the leaping head gave women the freedom to gallop, jump and hunt so it was fairly revolutionary. Before that you would either be stuck riding pillion behind a man or risking your neck.
Women started riding astride again around ww1 (well, I don't think Hey ever completely stopped but it became slightly more socially acceptable), when women were used to train remounts for the battlefield. At the same time I have heard of injured soldiers taking up sidesaddle in order to carry on riding after the war.
It's really interesting (I think) as it ties in with horses going from a manly, heroic, working, fighting animal to a 'girly' leisure pursuit - Susanna Forrest writes about this really well, and also not from memory in her pyjamas like I am 
. Equine sports now have a much higher female than male participation rate in many countries, despite women and men competing equally.