It sounds as if animal breeding is all in the hands of the humans. Compared to natural populations this indeed is the case, as we decide which animals are allowed offspring and which are not: selective breeding or in other words artificial selection. However, as in natural populations there is another force that plays an important role and that is the force of natural selection. In natural selection it is not us but the environment that determines survival and reproductive success of animals. So after we have decided which animals we intend as parents, they still need to be able to survive until reproductive age and to be able to reproduce successfully. As you can imagine, natural selection also results in directional change in the population average. Animals adapt to their environment and the ones who can do that best will be the most successful in survival and reproduction. In other words: in natural selection the direction of selection is on adaptation to the environment.
Even though animal breeding is defined as intentional selection by humans, you can see that natural selection will also play a role. In some cases natural selection will even work in the opposite direction of selective breeding. In those cases without human intervention the animals with the desired qualities will be less successful in surviving and/or producing offspring. For example, the fact that in many cows there is a negative relationship between high milk production and being able to get pregnant, shows that animals with the desired quality: high milk production, are less likely to produce offspring unless there is extra effort put into it by the farmer. Also, the fact that very high producing cows often have health problems indicates that their chance of producing offspring is reduced compared to their more average producing 'sisters'. Selective breeding often competes with natural selection. We have become so familiar to the fact that some of the best animals in a breed require assistance with some aspects of their survivability and/or reproduction that we think it is normal. Domestic animals are 'created' by humans and to maintain that we accept certain disadvantages. But how far should we go? For example, some breeds of dogs and beef cattle have been selected such that they are excessively broad in the head and/or shoulders. But being broad shouldered (or big headed) creates birth problems. Without human intervention such as assistance at delivery, or even a caesarean section, both mother and offspring would die. In other words: it is good to keep an eye on unwanted consequences of selective breeding.