As all of the other discussion here sort of reveals if you read it right, part of the problem is that the phrase "Survival of the fittest" is tautological. It might as well be "Survival of the survivaliest"; those who have the most "surviving" capabilities survive. On its own, that's meaningless, and indeed, it is often treated as a slogan more than science.

You had to add in genes for this to make any sense, an idea that we so thoroughly take for granted now that we can miss it entirely. Unless the organism has some intrinsic characteristics that contribute to its survival, and there's some sort of variation in the resulting children as it passes on the intrinsic characteristics somehow, you don't have anything like evolution. Then you get a non-tautological theory of how things can trend towards increased "survivalness", as you can demonstrate how constantly producing organisms with a spread of "survivalness" and lopping off the bottom can produce changes over time.