The consequence is you've destroyed a species and set a precedent and for what? One life?
While human life should be preserved whenever possible, there are situations where you must realize that human life is, from the perspective of our role as planetary stewards, cheap and disposable.
Sacrificing some lab animals, even thousands, to cure some obscure but crippling disease that affects a handful of people could be justified.
Wiping out an entire species to save a single person is atrocious, and completely insane.
If you're prepared to wipe out, say, otters to save one person then what's next? Elephants for another? What if it takes two or three species to save someone else. At what point do you stop?
Like would it be acceptable to kill all non-human life to save a single life? There must be some kind of line.
The "no consequence to humans" part is hugely subjective, but a case could be made that we're worse off than our ancestors because of how many species we've obliterated.