natural selection is wrong

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The white moth on the black tree was quite visible on the tree to predatory bird, and it was killed.

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In this case, specific camoflage is selected for. However, some white moths will reproduce, but many more black moths will reproduce. Camoflage is not directly related to the ability to reproduce, just the chances of reproducing and the chances of the offspring reproducing.

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The moths in this area died to chemical pollution caused by insecticides.

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. . . because none of the moths were resistant to the insecticides. They lacked the variation to resist poisoning resulting in local extinction. In this case, black or white camoflage had nothing to do with the selection process. I'm not sure if you are trying to say that natural selection is not applicable in this case, but it plainly is. The non-resistant moths were selected against. It just so happens that there were no organisms to select for.

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The moths flourished in the timeframe between the birds migrating south and the onset of winter.

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And those moth variants that are able to consume limited food supplies in a more effecient manner will out compete less effecient variants. Effecient food gathering will be selected for.

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The black moth took away the the insect the white moth was after.

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White or black doesn't matter. What is selected for is food gathering effeciency and food gathering technique.

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As before, a mutation occurs and it get's "tested" (sampling is not the right word yes) in terms of it's fitness to reproduce. Or the environment changes and the variations already present get retested. (but having the variation already present is not really the correct approach when the subject of interest is changes in structure of organisms).

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Umm, I think you might have slipped up here. For something to be "tested" it must already be present. Evolution is changes in allele frequency, that is the percentage of organisms with a specific trait. Yes, at some point in the past the specific characteristic or trait may not have been present, but to be tested it must already be present. And yes, under certain circumstances traits that were once selected against may become advantageous in a different environment. Just off the top of my head, predatory cats often go through cycles of long canine teeth followed by periods of short canine teeth. According to the most popular theories, this is due to a feedback loop between predator and prey size (both progressively get bigger over time until it is selected against due to environmental changes).

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1 or 0, illustrating that fundamentally the relationship of the organism to the environment in terms of reproduction, it's fitness, is a matter of reproduction or no reproduction of an organism.

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WRONG. It is the percentage of individuals with certain traits in subsequent generations. Using black and white moths, white moths will still reproduce and may make up a small percentage of the population even under strong selection. It is not a stringent "yes or no" type of deal. Black or white does not effect the actual ability to reproduce, but the ability to live long enough to out reproduce other organisms within the species. Also, fitness is not measured by how many "children" you have, but how many grandchildren you have.

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You can have evolution mean changes in frequencies, but you can't then use the theory of evolution to explain changes in structure of organisms, or sequences of changes in structure of organisms. To do that, you have to start with mutation.

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Mutations are just new alleles, and these new alleles vary in frequency with respect to their fitness within a certain environment. New mutations can create new structures, and these new structures are the variation which is then tested against the environment. "Changes in frequency" better describes the flow of variation through a population as compared to "descent with modification".

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I think it's signficant to note that you are disconnecting yourself from the realities of reproduction and mutation, by explaining in terms of populationshare. The population as a whole is reconstrued as one continuous organic body, which changes in response to the environment.

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I am not disconnecting myself from reality. In actuality, I am portraying what we observe in reality. Population share is exactly what we see. For instance, look at sickle cell anemia. In areas with endemic malaria the frequence of the sickle cell gene is high. In areas of no malaria, the frequency of this gene is quite low and usually directly attributed to migration out of malarial hotspots. Again, I am making claims based on OBSERVATION, which is a reflection of reality.Also, I am not claiming that a population is a single, organic body. If it were we would never observe instances of speciation. Speciation shows how new populations can form because of local variation and selection.

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Later on I did make an argument distinct from the authors about why it was faulty to separate natural selection from genetic drift into separate theories.
  —Syamsu

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I may have missed your argument, but I do want to comment on this position.Genetic drift is fitness neutral. Natural selection is a very important factor when looking at genetic drift. Think of it this way. What causes the accumulation of more neutral mutations within the population than beneficial or detrimental mutations?Firstly, detrimental mutations are directly filtered out through natural selection. This is pretty straightforward.Secondly, beneficial mutations are rare, and so their accumulation in the population should be less than both detrimental and neutral mutations. However, beneficial mutations are accumulated (ie kept) because of natural selection.Thirdly, neutral mutations are accumulated because they neither benefit nor harm the fitness of the individual. However, to determine if a mutation is neutral, it must FIRST pass through the filter of natural selection. A neutral mutation in one environment may be a beneficial or detrimental mutation in a different mutation. The only way to judge is to compare the new variant against the environment.So the effect of natural selection is to cause genetic drift through the disproportionate accumulation of neutral mutations. While genetic drift will not cause the ability to interbreed within the population, it might result in an inability to interbreed with other populations that were once interfertile. That is, genetic drift can result in speciation for a population that is split into two, isolated populations.