This is an ethical, not a legal, question first and foremost.
In 2002, the Netherlands legalized a limited form of euthanasia. Terminally ill patients in Holland now have a right to determine whether or not they wish to live. Parents of deformed or critically ill infants may be allowed to decide if they wish the infant to die.
The argument for euthanasia is that it gives humans the right to decide their deaths with dignity. The argument against euthanasia is that it is murder or killing.
People who belive that terminally ill people have the right to decide their fates still worry that legalizing euthanasia sets up a "slippery slope" that makes killing parts of the population, perhaps parts that take up resources or that others find unpleasant, to be much easier. That possibility has to be considered when discussing the issues.