Mosquitoes control human populations, an invasive species. Removing mosquitoes will make humans proliferate, which is known to be environmentally damaging.

Joking aside, the consensus seems to be that the effect of removing disease-carrying mosquitoes (not all mosquitoes) from the environment is minor compared to how many lives it can save.

Lots of animals eat mosquitos, but they really aren't the primary food source of any species, especially this particular type of mosquito. It would have a very minimal effect on food supply.

There are still a lot of other mosquito species. removing just the few that carry human disease will not have a major impact on creatures that eat mosquitoes.

Aedes aegypti is an invasive species native to Africa so removing it from the environment everywhere else in the world that it has been spread to would benefit the local mosquito species which don't spread the same diseases and are less of a nuisance to humans.

I believe the argument is the dominant mosquito species are themselves invasive to the continent

There are many mosquito species in competition for the same resources, only a few (iirc 10% in the US) of which sting humans and carry diseases. Wiping out the ones that attack people would allow other mosquitoes to take over the ecological niches.

The swallows love mosquitoes. When I get bit by mosquitoes I often joke I am feeding the birds.