Horses and donkeys are very close relatives, close enough that the chromosomal mismatch isn’t catastrophic.
Humans have no sufficiently close relatives, the other hominid lineages died out or got hybridized back in a long time ago.
The great apes are our closest living relatives, but they’re not *that* close anymore. It’s been at least 7 million years since the common ancestor.
Horses, Donkeys, and Zebras are all part of the same Genus, which is why they can produce offspring. Sheep and Goats are not the same genus, but are still closely related enough to mate although most offspring are stillborn.
Primates, however, are a very broad family amd as a result are more gentically diverse.
With apes, as others have mentioned, it’s because our last common ancestor was approximately 6 million years ago.
We were, however, able to breed with other hominids during the time hominids were developing. And later, when the homo sapiens subspecies developed, there is evidence that modern humans interbred with the recognized human subspecies: Neanderthals and Denisovans.
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