Crashfrog says that every species is in a state of transition. If humans are are in transition then how does resistance to disease make us mutate into a different species?
It doesn't. Reproductive isolation leads to new species, not mutation.
That article gives no examples of beneficial mutation that would lend to whole new species.
Because that's not how new species form. New species form through reproductive isolation. When two populations are separated from each other, and are constantly changing as all populations do, the lack of gene flow between them means that genetic incompatibility develops. They change in different genetic "directions" because the genetic communication (gene flow) between them is interrupted. As a result, they lose the ability to interbreed over time. That's how new species form.