I have yet to see any proof that one kind of animal can evolve to another. Sure there is mendellian variation but never any real evolution. Both sides dont really have any real proof.
Speciation is actually a very simple concept:
At the most basic level it is going to occur whenever two animals, formerly of the same species, can't or don't produce viable offspring. A common reason for this (allopatric speciation) is when two populations of the same species get geographically separated, so that members of each gene pool start to vary independently. Then if individuals later meet each other they can't (or don't) have offspring since they've diverged in some way - that can be as simple as size differences (imagine a dachshund trying to mate with a great dane) or even that individuals from the different populations just don't "fancy" each other any more (so they don't compete in each other's sexual selection market). That then isolates the two gene pools so that they continue to vary independently.
And yes, the scientific literature is full of evidence for this type of speciation including actual observation of speciation in the laboratory. You just have to look for it and leave your preconceptions behind. There is no proof in science, just overwhelming evidence.