What exactly is wrong with eugenics? Why is it so 'bad'?

Eugenics is not about wanting what's best for your child, it's about establishing yourself as the judge of what people are valuable and what people are garbage, and placing yourself in control of when the people you call "garbage" have children and with whom. Historically the eugenics movement has utilized forced sterilization, forced abortion, and even homicide to cleanse the population of undesirables. Do some reading about recent history and I think you'll see why it is considered such a dangerous and perverted philosophy.