[Elsie]

I don't see why we should be able to breed with them if they are indeed our evolutionary cousin.

Then, according to the predictive quality of the ToE, what is the mechanism that shuts off the breeding abilities between cousins?

[Elsie]

Breakfast time!

[bobdsmith]

Then, according to the predictive quality of the ToE, what is the mechanism that shuts off the breeding abilities between cousins?

Genetic divergance. The fact that two cousin species have diverged from a common ancestor species. Certain genetic differences will mean interbreeding impossible. This is seen in nature where very similar species cannot interbreed, or have some difficulty in interbreeding (lions and tigers for example).