We’ll start from the end of your question and work our way to the beginning. There is a huge difference between the patient not wanting the feeding tube and someone else removing it. The patient can refuse to eat. Some people just give up and that’s that. But no one else has the right to make that decision for the patient. The Church is adamant that the patient has the right to the ordinary means of preserving life: hydration and nourishment.
What your family did was to make your father as comfortable as possible and acquiesced to his wishes. This wasn’t even close to euthanasia. However, if for example, the doctors had introduced a chemical into your father’s body IN ORDER to cause him to die immediately, this would be the use of euthanasia.
This is what the Catechism of the Catholic Church has to say on the matter: “Whatever its motives and means, direct euthanasia consists in putting an end to the lives of handicapped, sick, or dying persons. It is morally unacceptable.
Thus an act or omission which, of itself or by intention, causes death in order to eliminate suffering constitutes a murder gravely contrary to the dignity of the human person and to the respect due to the living God, his creator. The error of judgment into which one can fall in good faith does not change the nature of this murderous act, which must always be forbidden and excluded. (#2277)
“Discontinuing medical procedures that are burdensome, dangerous, extraordinary, or disproportionate to the expected outcome can be legitimate; it is the refusal of “over-zealous treatment. Here one does not will to cause death; one’s inability to impede it is merely accepted. The decisions should be made by the patient if he is competent and able or, if not, by those legally entitled to act for the patient, whose reasonable will and legitimate interests must always be respected.” #(2278)
“Even if death is thought imminent, the ordinary care owed to a sick person cannot be legitimately interrupted. The use of painkillers to alleviate the sufferings of the dying, even at the risk of shortening their days, can be morally in conformity with human dignity if death is not willed as either and end or a means, but only foreseen and tolerated as inevitable. Palliative care is a special form of disinterested charity. As such it should be encouraged. (#2279)
Fr. Vincent Serpa, O.P.