First, it is not my classification system. The species that I list are all the accepted species names for these organisms. These have been decided by the scientific community, not by me. I've given you species names so you can check this out if you like.
You say that it is '[my] erroneous belief that separate species can interbreed.' It is not an erroneous belief. I have given you names of real species that can interbreed and produce fertile offspring. I've even given you examples of plants from whole different genuses that can crossbreed and produce fertile offspring.
Here's another one, backed up by a reference. The british freshwater fish roach and bream which are different species (not decided by me) can interbreed and produce fertile offspring. Depending on the history of hybridisation the hybrid fish may even have quite high fertility.
http://www.tandfonline.com/doi/abs/10.1080/10641269908951360
Here's the abstract.
Note the very relevant (to our discussion) words 'The validity of species concepts with reproductive isolation in their definition is questioned.'
There are loads of examples of different species (not decided by me) that can interbreed and produce fertile offspring (not made up by me). Hence, your whole argument that different species cannot breed and produce fertile offspring is demonstrably wrong.
You then discussed 'your claimed Darwin's Finches being separate species. I never said anything about Darwin's Finches, not anything about the Coelacanth, not about quite a few other things you then went on to, so I am going to ignore those irrelevant diversions in this post.
My point is that in selectively breeding both Great Danes and Pugs (replacing Pugs with Chihuahuas makes an even better example) we have produced organisms that are different enough that if they occurred in the wild we would call them different species. You have a counter-argument that since in theory they can produce fertile offspring they cannot be different species. I have given you examples that organisms are often grouped into different species even though they can (and do) hybridise and produce fertile offspring.
Broccoli and Brussel Sprouts are another example. If they were present in the wild, they would be called different species.
And there are examples where we have produced new species. Cross-breeding plants of different genuses have produced new plants of a different species. Finally genetic manipulation has produced a fruit fly of a new species. So, clearly we can and have produced new species.
The concept of a 'species' is far far, less clear-cut than you claim. And there are a LOT of organisms out there that we group into different species even though they are able to (and do) breed and produce fertile offspring. If we had discovered Great Danes and Pugs living in the natural world, we would have assigned them to different species.