Thoughtful selective breeding is obviously part of agriculture with both plants and animals. It is the responsible thing to do to not breed animals with known genetic diseases. Is this the same thing as eugenics in humans? After all, the same thing was suggested with humans that have genetic diseases.
I say that it is not, but before discussing that, I also say that most things eugenicists were concerned with, were not completely genetically determined, or genetically determined at all. Out of the things that were actually genetically determined, it was usually because of too many different genes for selection to be possible, and out of traits that did have simplistic associations with genes, it was arbitrary and biased to judge them as "good" or bad" traits.
The eugenics movement happened before we knew what DNA was. The exact mechanisms of how heredity worked were unknown. It was not possible to link a trait to a certain gene that could be detected in a person's DNA.
Eugenicists thought entire individuals were inferior or superior to others, and thought that an "inferior" individual would produce "inferior" children. In reality, children inherit thousands of distinct genes that each may or may not be expressed based upon the impacts of other genes and environmental factors. If genes truly were either "good" or "bad," each individual would have a combination of "good" and "bad" genes. But it would be impossible to tell by looking at outward characteristics whether an individual had certain "good" or "bad" genes, because not all of the genes would be expressed.
Even worse, if you selected an elite group of individuals you thought had "good" genes and made them reproduce only within themselves, "bad" genes you didn't know about would begin expressing, due to the gene pool becoming more similar. A smaller gene pool makes it more likely to inherit two copies of the same gene. With recessive genes, they are only expressed when there are two copies, meaning that generations of individuals can have ("carry") the gene without ever showing any effects. Until suddenly, two carriers have a child and that child happens to inherit the recessive copy from both parents, and out of nowhere, the gene starts having an effect. A lot of genetic diseases are like this.
(In this way, eugenics type thinking ironically contributes to genetic diseases, by assuming that restricted gene pools of only individuals that appear "superior" will reliably create offspring expressing the same "superior" traits.)
Of course, in all except a few scenarios (a high chance of breast cancer is probably bad), genes aren't inherently good or bad at all. Let's say you decided that tall people were genetically superior, and organized a club for tall people to get together and have tall kids. If you did this for generations and generations, your descendants might be able to become consistently extremely tall, but you would probably also find that being extremely tall could have negative effects in many situations. Tallness might be genetically linked to some positive things, but it would be just as likely to be genetically linked to negative things. If the tall people club was restricted from having children with people outside the club, eventually you would likely see a high incidence of genetic diseases being expressed due to inbreeding.
Animal breeding has been going on for millennia, but the preoccupation with "pure" breeds is much newer. Inbreeding has been practiced widely in development of breeds because that is basically the only way to quickly make sure the traits you want are consistently expressed in the offspring, but since there is no such thing as a "superior" animal, it's also a good way to accidentally perpetuate "bad" traits (such as a high risk of cancer) throughout an entire gene pool.
There is also the fact that whether genes are "good" or "bad" usually depends on the situation. There has been a MASSIVE loss of genetic diversity among livestock since the beginning of industrial farming, and this has been very bad because whenever something changes about farming--whether it's a new disease popping up, effects of climate change, or improved practices--genes that are helpful in the new state of affairs are hard to find, because so much diversity has been eliminated. You just don't know what impact a gene might have in the future. Imagine some kind of new virus emerges that cattle with a certain gene are particularly susceptible to. If your herd is genetically diverse, the incidence of the gene might be small, so you might only lose one or two cows. But if your herd is genetically similar, you might be losing half of your herd. Five minutes ago, those cows were the "best" cows! Not anymore.
Imagine how much more complicated it is with humans! Even within our lifetimes, different body types have become fashionable and "ideal" and different personality traits have become favored for the workplace. And we still haven't cracked the genetic basis of body type or personality, let alone the array of environmental factors that might contribute.
Ultimately the problem of eugenics is assuming that any entity "knows better" about whether someone should pass on their genes than the person themselves. Humans have the ability to understand genetic diseases and heredity for themselves, and choose to have children or not based upon their own judgment. Furthermore, humans have the ability to communicate their needs to other humans, understand disability in themselves and others, and care for disabled members of their own species, therefore optimal quality of life is possible.
It is hard to apply the concept of personal choice to other animals, since we can't give animals education on what actions can lead to or prevent reproduction or the ability to exercise choice in whether to reproduce. The reproductive biology of many of our domesticated species is such that they have an estrus cycle where they are driven to mate during the period of time when fertilization is possible. Humans do not have an estrus cycle and can engage or not engage in sex regardless of fertility. It is not a very good comparison.