As Charles Darwin said, survival of the fittest. As an intelligent species, we should not refrain from fighting back, but utilize our brainpower to our advantage. No mosquito thinks twice before biting a human, yet they're still apparently useful in some way. Humans need to stop thinking that it would be "unfair" to killing animals that are killing us in great numbers. As for any damage to the ecosystem, those animals simply need to adapt or die. Us as a species should not be banned from taking basic actions to preserve our own lives.
This blood-sucking creature could be eradicated without serious consequences for other species. Admittedly mosquitoes are prey for certain other creatures and they also pollinate some plants but there is no evidence to say that any one plant or animal relies solely on mosquitoes for its survival. Eradication of the species would, instead, save millions of lives around the world.
Pesticides are available that can significantly reduce or eradicate mosquitoes. Many deadly diseases are transmitted by these blood-sucking insects. To eradicate this species of pest is no different than wiping out smallpox, AIDS, cancer or any other deadly disease. The viruses of these diseases are living organisms. Mosquitoes have no redeeming value.
No we should not simply because that would mess up the nature. The food chain from small to big, dangerous to harmless would not work if you took one single animal out of that... There's a reason why it's named "food :::chain:::" it's a chain. With one single piece gone or destroyed it won't work.
We should not eradicate mosquitoes because they provide a vital part in the worldwide food chain. Although they cause much harm to humans eradicating them would be the wrong thing to do for the world. Many animals live off of mosquitoes and there would be many unforeseeable effects if they were eradicated.
We should do things to eliminate the disease threat caused by mosquitoes, but the destruction of any species disrupts the ecosystem. Bats eat thousands of mosquitoes a night, and other species consider mosquitoes food. If we eradicate the food source we may end up also killing off other species. Not for us to make that decision.