In Parshat Kedoshim the Torah prohibits three different forms of kilayim, crossbreeding:
You shall observe My laws. You shall not let your cattle mate with a different kind; you shall not sow your field with two kinds of seed; you shall not put on cloth from a mixture of two kinds of material. (Yayikra 19:19)
Previously, in Vayikra 30:38, the Bechor Shor elaborated on the rational for the prohibition of shatnez, the mixture of two kinds of materials, which he mentions here as well. Since the special clothing of the Kohanim contained shatnez, non-kohanim are prohibited to wear shatnez as a means of reserving and elevating such material for only holy purposes. (One could argue that this is why the only non-kohen garment that is allowed to have shatnez is Tzitzit, due to its uniquely elevated status as a garment.) In this sense the prohibition of wearing shatnez is, for the Bechor Shor, similar in function as the prohibition of consuming blood, as noted in Parshat Shemini. Both prohibitions are intended to elevate the prohibited item, rather than denigrate it as is the case with items which are tameh, ritually impure. (See the Bechor Shor in Shemini for more on this.)
The Bechor Shor presents a very different approach for the prohibition of cross breeding animals. The prohibition is introduced in the Torah with the words, “You shall observe My laws.” Which laws does the verse refer to? The Bechor Shor writes that it is referring not to the laws of the Torah, but rather to the laws of nature. This is certainly not a typical way of reading the word laws!
Accordingly, the Bechor Shor writes that God created the world with certain laws of nature and He does not want humanity to attempt to alter those laws. One such law of nature is how animals mate with each other. Species mate within their own kind and do not mate with animals from another species. Therefore we are not allowed to cross breed animals from different species because God did not intend for that to ever happen. Had God wanted different species to be able to mate with each other, He would have created that in the natural order of this world.
In the book of Bereishit (Bereishit 1:22, 8:17) God blessed the animals that He created and charged them with peru urevu, reproduction. However the Bechor Shor writes that this blessing never extended to the animals which do not naturally mate with each other. This is why when two animals from different species are in fact cross mated, the resulting hybrid animal is sterile. What we know to be true from genetics, or observation on the farm as was most likely the case in the middle ages, the Bechor Shor has validated and provided the deeper spiritual meaning from the Torah.
We live in a world wherein technological innovation is rapid and pervasive. We gladly make use of these developments, but the Bechor Shor is reminding us to know our place in the world and to not overstep our role.