Why do queen hecuba and king priam decide to kill their child?

Because of a dream that pregnant Hecuba had one night, in which her child was a torch. Aesacus, a prophet, gave her an interpretation: her son Paris would cause the ruin of their great city of Troy. To prevent this impending doom, Aesacus told the royal couple, the child has to be killed. However, Hecuba and Priam didn't have the heart to do it, so they gave the child to a shepherd. The shepherd also couldn't do it himself, but let him in the mountain to starve. So, Paris survived, and the ruin of Troy was imminent.