Would you get your kid out if you didn't know whether or not they would be adequately cared for? Would you get them out if it meant that you will probably never see them again and that they will be taken to another country speaking another language with no one there to look after them and no plan for how to take care of them after the medical treatment is done?
This would most likely be a permanent separation and the child would effectively, or maybe even literally become an orphan in a foreign country with nothing. Not their vital documents, not their family, not anything that would give them any hope of ever getting home. Getting your kid out in this situation means gambling your child's life on the good will of strangers and most likely losing them for good.
It is not unreasonable to demand to go with his child. Especially since he needs medical care as well.