Why is it that different species can not reproduce with eachother?
Because that's the definition of what it means to be "different species".
THe technical term is reproductive isolation. The root cause is that their genes are too different, but this can produce various different effective causes. Perhaps the members of the species will just not look attractive to each other. And if the members do mate (or are forced to mate in the laboratory) the different genes may make it impossible for a viable zygote (initial single cell of the offspring) to form, or if formed to successfully attach to the placenta (in mammals), or if attached to successfull develop thorugh all the stages of embryology.
Some species, such as horses and asses, are close enough to produce a viable offspring (mule or hinny), but those offspring are then sterile.
Mutation and selection do tend to produce reproductive isolation, and human scholars then use reproductive isolation to define species, but that definition is not quite perfect. There are several cases of organisms which exist in populations spread out in a line like beads on a string. Each population will breed fertilely with its neighbors on either side, but the two populations at the end of the "string" are reproductively isolated. How many species is that? Or consider my ever-recurring example of North American canids. Wolves, coyotes, domestic pooches, none of them entirely reproductively isolated from the others.
I have always wondered about how this happens. What exactly explains that they can reproduce but necessarily have sterile offsprings? What is the exact mechanism for that to happen? It is fascinating that such a situation could occur. It would seem that either reproduction would be impossibel *or* it would lead to viable offsprings (viable in the sense of able to reproduce themselves). How does this work?
That is extremely interesting. I didn't even know that horses and donkeys could produce offspring. I thought mules were a species of their own. What other combinations of species can create sterile offspring like that?
Once again I turn to handy Wikipedia ;)
The term you are looking for is "Hybrid": http://en.wikipedia.org/wiki/Hybrid
Separate names with a comma.