Unfortunately, this is nature. The parents know that something is wrong with the cygnet. In fact, all three may have been ill or attacked by a predator and severely injured. Instead of risking a predator getting the cygnet, especially a human, the parents will kill it to put it out of its misery. It does not take long for a young swan to be killed, especially, when the male parent grabs it by its neck and slings it around.

If these were young parents, the cause may have been that they did not understand what was going on with a pesky screaming creature constantly following them around. Since these seem to be seasoned parents, then it probably was an illness or injury. The Regal Swan