I have looking online to find answer to this question and one answer said that the tail increases drag and weight but, it did not say why the Increase in drag makes the kite stable. One theory I have is whenever the kite try's to turn left or right with a tail, the tail creates drag and pushes the kite the other way but, I am not sure
The tail adds drag in a particular direction. Kites are designed to fly with one side facing forward. The tail orients the kite by dragging on the opposite side. Fixed wing aircraft in general include tails that work almost the same way, by creating horizontal lift to pull the craft back in line when it begins to yaw. One notable exception is the B-2 Spirit stealth bomber, which has no vertical tail but does use an automated input system to help control the plane.