Wouldnt that be more to do with the appearance of the sangha to the wider society?A bhikkhu, out of compassion, once said to an Execution, “Kill him with one blow.” The execution did as the bhikkhu said. They reported this matter to the Blessed One, who told the bhikkhu: “You have fallen into an offence of defeat.”
The motivation to heal it would could also be rooted in aversion to the birds suffering (and so be unwholesome) but is classed as wholesome. Yet the want to kill it to put it out of suffering (the same motivation to alleviate it's suffering by healing) is unwholesome?The volition at the moment of killing is rooted in aversion (dosa), so it is unwholesome kamma. The right thing to do is to take the bird from the cat, put it in a quiet and safe place, and leave it to die of it's injuries (if you don't have the skill to heal it).
The outcome is always the same. One scenario has less dukkha and the other scenario has more, but the one with less dukkha is morally wrong and the one with more dukkha is right?