Is the Prophetic Hadith: "Were dogs not a nation among the nations created by Allah, I would have commanded their killing; so kill every jet-black one among them" authentic? And why was the killing of jet-black dogs commanded?

The Prophet (peace be upon him) commanded the killing of all dogs, but this command was later abrogated, except for three types:

1. The jet-black dog (al-kalb al-aswad al-baheem): This is a dog that is pure black with no other color mixed in, and it has two white spots above its eyes. 2. The black dog with two white spots: The killing of other types of dogs was prohibited. 3. The rabid/vicious dog (al-kalb al-aqoor): This refers to any dog that bites people and frightens them.

It is permissible to kill these types of dogs due to the harm they cause, while the general narrations that commanded the killing of dogs were abrogated, except for what was specifically excluded.