Here's the deal:
Mosquitoes' survival requires water. Not just in terms of drinking. Throughout their life cycle these blood robbers experience the 4 typical for all flies stages of development - egg, larval, pupal and adult. The adults are the ones that fly around and recklessly feed on human blood in their savage manner. But the three other stages are entirely developed in water. Stagnant fresh water that is. And what is the most common place in your home with stagnant fresh water? Correct - the clogged gutters you refuse to unplug and clean. But no one blames you - it's not an easy job to clean gutters, it requires ladders and a brave heart.
Female mosquitoes seek either stagnant waters or aquatic plants to lay their eggs in/on. The first 5 to 14 days of a mosquito's life cycle is spent entirely in water. Larvae hatch and feed on microorganisms underwater, then they become pupae inside of which the glorious adult mosquitoes grow and later on gallantly emerge.
Having time to nicely rot, all the leaves that were actually the reason for your gutters to get clogged in the first place are now providing the innocent larvae with all they would ever need as a food resource. And all of this happens right above your window. Probably right now, while you're reading this.