First off, could you give me any proof that humans are not evolving? I would love to see it. That's sort of like asking why we don't see the Milky Way change shape in the sky even though it's spinning. It's too slow for us to observe on the time scales we experience. Humans are biologically indistinguishable from the way they were 200,000 years ago. By contrast, civilization has been around for 5,000 years.

I do agree with you partially in that humans have slowed down their evolution, but this can be explained without tossing natural selection out the window. We simply like to save everybody. Modern people have developed a society that wants to spare everybody's life if possible (with certain extreme circumstances, but you get the point). If people have non-beneficial genetic conditions that they can live with using the help of civilization but they would otherwise die in the wild, they are allowed to spread those genes and the gene pool for humans doesn't really develop much. Most modern humans, barring extreme circumstances, survive well into their reproductive years, so the next generation's genes will be pretty much the same as this generation's. Also, our choice of mates is no longer "how biologically fit is my mate?" but a question of personality, something far more relevant for humans than for animals.