The distinction is important because it means that there probably won't be an ecological imbalance if we exterminate the mosquitoes, since there are no species that exclusively depend on them, or which they are responsible for keeping in check.
When you eliminate a native species, the unintended consequences can be wide.
This makes the weird assumption that a non-native species will never occupy any position within the local ecology. Consider a (slightly unintuitive) case of an intrusion into a well-established ecology: maize into human society. Europeans came to America with a level of reliance on maize of exactly zero, since they weren't aware it existed. They brought their own grains. And we grow wheat here today. But... if we decided to completely eliminate maize, would there be any consequences for American society? Or for a case with more historical flavor, consider the introduction of the potato to Ireland. There were problems when the potato population failed.
More generally, if species I ("intrusive") arrives and replaces species A ("autochthonous"), why is removing species I more dangerous than removing species A would have been?
