What was or would be Aquinas’ argument regarding active euthanasia?
Many people have asked about this, and unfortunately, Aquinas does not deal with euthanasia directly. Aquinas does address whether, in certain circumstances, homicide might be permissible (ST II-II, q. 64). Specifically, it is not wrong to kill a person in order to preserve one’s life so long as one does not intend to kill, but only to save one’s life and one uses moderate force (a. 7). The one who has care for the good of the community may also kill an evil-doer if he or she is a threat to the community (a. 2). (This is the same rationale by which he says that it is permissible for heretics to be executed. See the question concerning capital punishment and the essay on tolerance.)
Aquinas also makes allowances for killing an enemy if one is fighting in a just war, and his reasoning is similar to the case of civil authorities killing evil-doers. As far as I know, these are the only reasons one should have for killing a person, which Aquinas believes to be, in general, a very bad thing. I don’t see how he could condone killing someone because he or she suffered from a painful, debilitating illness.
Generally, one kills only to preserve human life (that of an individual or of a community). Since he is a Christian, I think, too, that Aquinas would believe that the killing of someone who is suffering deprives them of a chance to find in their suffering God’s redemptive grace. It would be wrong, then, both as opposing the natural good of life, and the supernatural good of redemptive grace.