Question

We can hear the movement of a mosquito's wing but we cannot hear the movement of our hands

Answer 1

because the number of vibrations of a mosquito wing is more than that of our hands

Answer 2

Mosquitoes wings are vibrating at such a frequency that our ears are sensitive to hearing, up in the 10 kHz region. Besides, they seem to like flying near our ears which supports the make up for the small amplitude of sound. But our hands can hardly flap at a few hertz that is too low to be heard.