How is it permissible to kill harmless dogs, even though they have a benefit in environmental balance, and why did Allah create them? Is it permissible to kill cats and dogs that steal food, given that they are living beings acting out of hunger? Is feeding them considered lawful (halal) or unlawful (haram) sustenance? And does my statement to my mother, "There is no issue that carries both prohibition and permissibility," make me an apostate, knowing that there are different opinions between permissibility, prohibition, and detestability regarding the issue of killing harmless dogs?

Scholars have differed on the ruling concerning killing harmless dogs. Some permit it, arguing that they are of no benefit, may cause harm, and decrease the reward of their owner. Others dislike it, while some have gone as far as to prohibit it.

As for killing animals created by Allah, the permissibility of killing dogs does not contradict ecological balance, nor does it mean annihilating all dogs. It is illogical to claim that nothing created by Allah may be killed, as harmful predators may be killed.

Regarding killing cats that steal, it is permissible to kill a cat if it causes extraordinary harm that cannot be repelled except by killing. What you mentioned is emotional talk without proof.

As for letting them take something from you with the intention of feeding them or seeking reward from Allah for it, there is no sin upon you in that; rather, you are hoped to receive reward and recompense. Feeding animals is among the doors of goodness, and in the Hadith: "In every wet liver there is a reward."

As for your statement to your mother: "There is no issue that combines both prohibition and permissibility," there is nothing in it that necessitates disbelief.