A Brief Intro
During any conversation about genetic engineering, people inevitably bring up worries about eugenics movements of the past and often use the cruelty, bad science, and objective failure of these efforts as an example of why we shouldn't ever try anything remotely related again. In this short post, I'm going to summarize why I think selective breeding of humans is bad both from a moral perspective and ineffective as a means of improving human genes.
Selective breeding at its core involves taking organisms that score well on some test of desirable traits and enabling them to reproduce at higher rates than organisms that score poorly. Despite its many flaws, this technique has lead to amazing gains in both agriculture and animal husbandry, and allowed domesticated corn crops to undergo this incredible transformation over the last few thousand years. 
But despite the amazing performance on crops, there are reasons this technique would not work very well on humans.
Humans are Slow Breeders
Every generation that you selectively breed an organism you get some gain in a particular trait. The faster reproduction happens, the faster you see improvements in the trait(s) under selection. Humans are extremely slow-breeding animals. Though humans are capable of reproducing sometime in early adolescence, most humans today opt to wait until their 20's to 30's to have children. This is a very very long time if you want to do selective breeding.
Selective Breeding Leads to an Undesirable Reduction in Genetic Diversity
Genetic diversity is valuable. Because selective breeding can only work by throwing entire organisms out of the gene pool, it naturally ends up reducing a lot of desirable genetic diversity. Even organisms that don't score well overall will still have many good genes. With selective breeding, there is no way to keep this valuable genetic diversity unless one were to select the best X% from every lineage in a population.
Selective Breeding Creates a Single Point of Failure
The right to reproduce is foundational to all modern societies. Even in societies that do place restrictions on reproduction, such as China with its one-child policy, the restrictions are not total: each couple can still have a single child. In order to make any notable gains in desirable traits from selective breeding, one must necessarily only allow a small portion of the population to reproduce. This would require an incredible concentration of power in the regulatory authority, and the pressure on regulatory officials from powerful people who want to be able to have children would be immense. I see rampant corruption as nearly inevitable in such a system.
Not only that, but concentrating power in this way creates a single point of failure. It is not too difficult to imagine such a system becoming corrupted by discriminatory ideology. In fact, you don't even have to imagine it because this type of failure was exactly what happened in Nazi Germany before and during World War II when they implemented a eugenics program based on racist ideology and belief in a fictional Aryan "master race".
Selective Breeding is Cruel
For myself personally, this is the most compelling reason to not use selective breeding: it is a cruel judgment upon those who, through no fault of their own, happen to draw the short stick in the genetic lottery. The desire to see some part of ourselves live on past our death is nearly universal, and the most common realization of this desire is through having children. Restricting this ability, even if it would result in future generations more capable of carrying on the human legacy, would be an enormous price to pay.
Though we may recognize that certain genes confer advantages to an individual, we must not confuse human ability with human value. As humanity enters the age in which we will be able to rewrite our genetic source code, I think this is one of the most important lessons for us to remember.
As a side note, here's the succinct algorithm I thought of the "clean up" the human genome.
For each allele:
Sample across the population, find the prevalence of different versions of the allele
Expected : most alleles are going to be either [99% version A][1% or slightly mutated A]
Take version A, the other versions are incorrect
Some Alleles will be in the form of [40% version A][50% version B] [10% mutated versions of A or B]
In this case, look at the data and try to see if A or B is statistically correlated with a desirable trait. If you can't determine, choose the version the parents of this designer baby have.
And that's it. You don't need to know what most of the genes do. Statistically speaking you are going to almost always be right with this algorithm, the resulting baby will not be uber but will not have as many problems as baseline humanity, because by simple probability, most mutations are neutral or deleterious, and a significantly beneficial mutation will have a prevalence greater than 1%.
It may be safe from an individual perspective, but if you always pick the more common allele, you are converging towards the modal genome, which would be a world where everyone is a clone of everyone else.
Genetic diversity is valuable both as a hedge against disease and because it lends itself to specialization, which is an important part of the modern economy.