Tons of comments, but no answer from an actual horse.

Why do the proletariat allow the bourgeoisie to ride on their backs?

Because riding on their fronts is too intimate.

They get trained. Think about humans for example. There's lots of stuff we don't think twice about doing that aren't necessarily things we would naturally do; they're taught to us socially and we get used to them as part of life. Horses were domesticated, firstly selectively bred to be friendlier to humans and faster, but secondly they still get trained to form a bond with humans and to do what humans want them to do. They get used to being ridden.

Cows didn't let us ride them, and look what we did to them... Look what we did to them!!!

Because when they tried to ride humans they would break them.

they are domesticated. if you were trying to ride a zebra they will likely attack you instead, because they are still wild and havnt been domesticated.

The same reasons dogs work for us. They are domesticated animals, selective breeding for thousands of years. Then training, teach them when they are young to do complex tasks. They then enjoy the tasks because it makes us happy. Think of sled dogs, or seeing eye dogs. Not exactly a natural thing for them, but once they are trained they really enjoy it.

I used to watch this video two years ago, and a few other horse history video on that channel https://www.youtube.com/watch?v=AMHqp0M0T4Q

It's a more approachable video for general audience so it may not be super scientific. But they included the source/papers in the description from proper academics.

Wild horses were originally not fit for riding. It is found that their bones would not be able to support to be ridden. But at the time, horses also started interacting with human & being domesticated as food & material sources.

But human do realize the power horses have. Human started developing chariots to be pulled by horses. The chariot technology spread around the north eurasian steppe to south in the south-west asia & egypt. But I cannot definitively say if the chariot techbology in egypt or persia came from north or it's developed locally. I haven't exactly find out about the relationship of both region when it comes to chariot technology.

During few thousand years later horses also slowly evolved physicaly to be able to be ridden. And so in later bronze age, nomadic steppe people emerges such as the Saka/Scythians, Xiongnu, etc.

My personal searching two years ago was definitely very focused on central asia/eurasian steppe region. So I cannot say much about the same stuff happening in south-west asia despite I know there are a lot going on in that area at the same time. But then after writing this and re-read the question, this doesn't exactly answer why horses allow human to ride them 🤣🤣 I only say about how human changed horse.

I'm pulling this from some random place in my head but horses have a strict hierarchy. There's a head horse that runs first and people became the head horse. This is in stark contrast to zebras that don't give a shit and cause chaos.

My guess would be evolution. Those horses that let us ride them were fed well and cared for by humans and then mated with similar horses to make more and more of the same. Those that didn't let us ride them had to fight for their own food and fight for their own mates and didn't multiply as much. So we essentially happened upon a couple of horses that enjoyed hauling us around, told them to kiss each other, and we got more. Repeat and rinse for tens of thousands of year.

They are forced into submission through a process of violence and psychological torture their abusers call "breaking". They have also been selectively bred for docile traits.

Horses that resist this process and don't allow their owner to ride them will eventually be written off as being "unsound" and euthanized for whatever excuse they can diagnose them with.

the horse contains the spirit of the rider's dead mom obviously

We have food