I used to think that was how it worked as well, until I read more about it. Think about the definition of the word "species". It is vaguely defined. The reason it is vague is that sometimes closely related animals can interbreed, and sometimes they can't, and so it is hard to draw the line between two species. The theory of evolution does not require a huge jump from one species to another. Rather, it implies small changes in each generation. These small changes are not usually enough to prevent reproduction.
After enough time however, these changes build up, and reproduction becomes impossible, or flawed. This is why horses and donkeys produce sterile mules as their offspring. If they were more closely related, the mule would be able to breed with horses or donkeys. If they were less closely related, no mules would be born at all.
Given a few thousand more years, maybe donkeys and horses will no longer be able to interbreed and make any mules at all. This is because too many changes (mutations) have built up.