The non-sequitur argument is the notion that species "have a right to exist". The only species that conceives of such things as "rights" are homosapiens. Minus our species, there are no rights, only nature. Species come and go without notice when humans aren't around to observe them.
Species can adapt to changing environment, or not. We can value their existence or not. I don't like mosquitos, and if I could, would eliminate them all. I value birds only insofar as I like that it gives some people joy to observe them, and some of them are tasty. Hummingbirds are neat. My everyday interaction with birds is usually something along the lines of washing their poop off something. Not a fan in general.
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