You could ask the same question about all sorts of parasites (ticks, tapeworms, etc.), but I think the answer is pretty clear. It's not the conundrum you think it is, and the vast majority of people correctly see no contradiction between killing a mosquito that's on their arm drawing blood and agreeing that mosquitoes are a relevant part of the ecosystem that should not disappear entirely.

Animal rights people saying you cannot kill mosquitos for ethical reasons is such a small minority, I guess it must be lower than 0.0001%

Most vegans and vegetarians I know choose that lifestyle because they see a problem in the ecological and environmental implications of eating meat and for political reasons of how animals are kept.

Have you seen how intensive animal farming works in practice? Even as a meat eater one must admit the conditions are cruel. I don't think we do this with mosquitos.

Who wants to eat mosquitoes anyway

Jainism. It's ancient and worried about small lifeforms we can't see since before we identified bacteria or used a microscope.

Why mosquitoes? Cats are right there. They're obligate carnivores.
But I don't see that as the point, the point is that we as an (supposedly) intelligent species can choose not to murder a quarter of a billion chickens every 24 hours, and that we can replace what nutrients we get from meat with mineral, plant or fungi alternatives.

There's a difference between protecting yourself from a parasite species which spreads deadly diseases and torturing an intelligent being for no reason. Happy animals taste better, you know.

This isn't really the gotcha you think it is. Killing mosquitos is self defense, it isn't comparable in any way to killing innocent animals which have done nothing to you.

Gee gosh what a clever point that nobody has thought of before. You're the first one! Those silly animal rights people should just give up everything they believe in now that you've totally destroyed the logic of what they've thought about way to much compared to how much you've thought about it. You've exposed their hypocrisy. If they can't do everything exactly perfect, what's the point of trying to make anything better, right? Anybody that aims for anything less than extremism doesn't really exist anyway; everybody thinks in black and white. Thank you thank you thank you for your thoughtful contributions on this subject that turns out to be really simple. Everybody else that allows for any sort of nuance is dumb compared to you with your single clever point that brings the whole thing down. Why would anybody even bother going any deeper into this than you already have since you've solved the whole thing?