Another perspective view to look at is what happens when a person is kept on life support when they have no chance at recovery.
For every hour that someone spends in a hospital bed, is an hour that bed must be denied to another patient. Every minute on a ventilator or with a machine pumping their blood is a minute those machines cannot be helping someone else out there who needs them. Every second during which a nurse or doctor must administer 'care' to the child is a second they cannot help another person. Even the food and water that they send down the persons throat or in through a feeding gastric tube cannot be used to feed or hydrate someone else.