But that doesn't mean it's “irresponsible” or otherwise unseemly for someone else to put down the animal, especially in your presence. That implied insult is unnecessary.
Of course, that wasn't the point of “unwilling”. Complete non-sequitur. The “unwilling” in this story had to do with caring for the animal, giving it all the surgery it (supposedly) needed; not disposing of it.
BTTT, in agreement, with all you said...