Now, the nature of this companionship tends to form really strong bonds between centaur and their rider, since they literally have to protect each other's backs.
Thing is, when I take a creature from a mythology, I also tend to lift "background" elements from it, for flavor, which means that bisexuality is the norm here.
So, centaur and rider are bound to get more close and lovey dovey in the downtime. While the human "riding" the centaur should be safe, the reverse is most definitely not, just look at the story of Mr.Hands (NSFW).
The army wants to avoid such embarrassing and unnecessary casualties and since people will be people, they know they can't really stop them, plus it does seem to have positive effects on the morale (and don't ask why is there a Wikipedia article about this)
The best way to deal with this problem is to make sure that at least if they do it, they do it safe (finding contraceptives isn't an issue, internal bleeding is). But how can a reverse ride be made safe for a human?
Since the budget, as well the number of desperate engineers with no sense of shame are limited and because it's a private thing, it'd be preferable if this safe way didn't require any tools or extra people.
As far as anatomy goes, they are... strange. Two hearts is nothing new. The human and horse spines are joined with an L junction that's made up of many small vertebra that get progressively fewer an larger with distance from the L junction. The rib cage is kind of wacky as well, since it has to bear the load that is the human torso. I can't really describe it, but it's obviously very different than what a horse has.
The human part has a stripped down digestive system, while the horse part is modified to be able to digest meat and now has a much stronger gastric acid and more enzymes to nuke the million and one digestive diseases that a horse can get.
The horse part has a height of 155-165 cm at the withers.
Centaurs breathe through their mouths during intense exercise and are generally lower-speed endurance runners with decent sprint-bursts. They also like to cosplay as Polish winged hussars.