Why is natural selection not the survival of the fittest?
"Survival of the fittest" is a term that is used inappropriately.
Natural selection refers to the process by which organisms evolve. There are selective pressures in their environment that affect reproductive success.
For example, a mouse that lives in an area with black rocks can have babies with dark colored fur or babies with light colored fur. The mice born with light colored fur are more likely to be eaten by predatory hawks because they can be seen more easily against the dark background. The dark colored mice are less likely to be seen as easily and will live longer to reproduce more. The more the dark colored mice reproduce, a larger portion of the population will become dark colored and the allele frequency of the population shifts to favor dark colored fur.
In this instance, the dark colored mouse is said to have higher reproductive fitness since it is more likely to reproduce more in this environment. "Survival of the fittest" is a phrase that is related to this idea of reproductive fitness, but doesn't really mean what most people that use it think. Those people are usually thinking of intelligence or physical strength. Fitness affects the survival of alleles and genetic material, but not the survival of the organism.