There could be several reasons. If the parents are new parents, they may not understand having something so little hang around them and they may react accordingly.

If there is something wrong with the cygnet, the parents will try to put it out of its misery.

If the cygnet is sick, the parents will not risk having a disease spread to the family or the entire flock and will try to remove the threat from the habitat by killing the offspring.

If the cygnet is sick or injured, it may not survive because of these reasons, but the illness or injury may also cause the young bird to act abnormally, keep it from staying with the family and in doing so, attract a predator to the family or flock.

Nature is not kind to sick or injured wildlife. Feeble, weak or dying animals/birds cannot do what is meant for them to do, propagate the species. If they cannot add good genetic material due to an illness or injury, or have the opportunity to kill other members of the species through disease, nature will not allow them to survive. The parent swans would rather kill their young then to have a predator take it, including humans. The Regal Swan