Why are mules sterile?

First thing you have to realise is that all mules are NOT sterile. Most mules certainly are, but there have been numerous authenticated accounts of mules giving birth to perfectly healthy foals.

Next thing to do is to ignore those people saying that it is because they are hybrids or because horses and donkeys are different species. Numerous species are perfectly interfertile despite being far more distantly related than horses and donkeys and having far more widely differing chromosomes numbers.

Thirdly ignore those people saying that mules are clones. Mules are the product of sexual reporduction. If they were clones then by definition they would be either entirely horses or entirely donkeys.

And finally mules have perfectly functional reproductive organs so that isn't the reaosn.

So why are mules sterile?

That’s pretty complicated and to be quite honest we still don’t know the whole story. The basic problem is that after the ancestors of donkeys and horses split the chromosomes of BOTH species fused and then those fused chromosomes re-split. That has led to a situation where the information originally carried on a single chromosome in the ancestral species is now found on 2 different chromosomes in mules and 2 totally unrelated chromosomes in horses.

Normally a developing foal embryo would receive two copies of each piece of genetic information: one from the mother and one from the father. In the case of a mule foal it receives a random number of copies. It will receive three copies of some pieces of information: 2 from the mule parent and one from the horse/donkey parent, or it will receive only a single copy from the horse/donkey parent.

Because of that mismatch of genetic material the embryo has a hard time developing. Some traits it will lack sufficient information for since it has only half the required genetic information, while other traits will be overdeveloped because there are 3 or more genes where there should be only two. All mules will get pregnant if mated, but the embryo develops for just a few days and then dies because it lacks the correct genetic instruction to develop further.