That is an oversimplification. Numerous examples have been given of more complex categorizations. You have yet to address any of the examples. Genes can shorten the life of an individual, even prevent individuals from breeding, and still benefit the species. Selection operates on populations.
What kind of shell game is this, anyways? Think about a gene like the one mentioned above. Is it one you would like to have? Are you unable, on the basis of its general effect, to categorize it as any of the following:
a. beneficial
b. neutral
c. deleterious
Does an operative principle intended to result in a survivable population introduce a gene that shortens life and does not allow for reproduction? To most folks with a little common sense a gene such as this would be considered "deleterious."
It certainly goes against the operating principles of natural selection as an agent opting in favor of beneficial genes so essential to all the progress we've enjoyed for these "billions" of years. Otherwise, if natural selection operates without principle and can be arbitrary, then what is it's value other than pretending it was operative as we describe the past?
Amazing. Populations are a description or a grouping. They are like the forest. The forest is made of real things called trees. Selection works on individuals. Living things die. Populations disappear or become extinct when the all of the things they consist of become something else or die. Gosh you are simply desperate to deny the weaknesses of the theory.