It is a hobby of mine to hunt flies in the air by beating them with a small piece of wood. Is this impermissible because it hurts the flies? Thank you.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

It is known that flies are a major reason for the transmission of diseases; rather, they are one of the most harmful types of insects. Given their harm, it is permissible under Sharee‘ah to kill flies in order to avoid harm. It is narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said: "If a fly falls into one of your containers [of food or drink], immerse it completely before removing it, for under one of its wings there is disease and under the other there is (its) remedy." [Al-Bukhari]

Al-‘Atheem-’Aabaadi said: "The Hadeeth is an apparent proof that it is permissible to kill flies to avoid harm."

It is clear that immersing is more severe than beating when killing, yet the Sharee‘ah did not prevent it. Nevertheless, we advise you to utilize your time to do what is beneficial for you in the two worlds, instead of wasting it in hunting flies.