The spaying of animals, in order to prevent undesired reproduction or in order to make them more docile, is an ancient custom of animal husbandry, but it is one which is forbidden by the Torah. The Torah teaches this prohibition in two different places, each one with its message.
In the blessing given to Noach and his family after the flood, "Be fruitful and multiply, swarm in the earth and multiply in it" (Bereshit 9:7), our Sages discerned an implication that spaying of animals is improper for all mankind (Sanhedrin 57a). The basis of this admonition is clearly the fact that spaying interferes with HaShem's desire that the world should be filled with a multiplicity of living things. Here the consideration is a quantitative one.
However, the Torah also contains a prohibition on spaying for the Jewish people. In enumeration the animals which are blemished and unfit for sacrifices, the Torah tells us (Vayikra 22:24) "And an animal which is maimed or crushed or disconnected or severed [in his reproductive organs] do not offer to HaShem", and then adds "and don't do this in your land", meaning that we should not create such a blemish (Shabbat 110b).
Here the emphasis is not on the consequences for the world, but rather the consequences for this particular animal. The blemish in a sacrifice is not due to the fact that the animal will not reproduce, because the animal is being slaughtered anyway. Rather, the admonition not to spay seems to be directed at the loss for the individual. Each individual creature is unique, and its ability to transmit its own unique characteristics to offspring is an essential part of its character and potential. Even if the world will swarm with sheep just as before, this individual ram is deficient if he lacks the potential to perpetuate his special traits in the next generation.
This distinction between the general mission of mankind and the particular mission of the Jewish people is found in other places as well. For instance, in our column on Vayikra 5761 we saw the explanation of Rav Nachman of Breslav, that for all mankind ownership and possession has utilitarian value, but for the Jewish people ownership also ideally involves a special sensitivity to the unique role of each object in the chain of Divine providence.
All of mankind is charged with perfecting the world, both materially and spiritually. But the mission of mankind as a whole is more instrumental, focusing on principles which create a better world. It is the Jewish people who are particularly commanded to find the holiness and potential in each individual aspect of creation, "so that none of them may be rejected" from the realm of holiness. (See Shmuel II 14:14.)