OK Gnu, let's talk about this then, shall we?
If you really must kill animals for your own self-gratification, then at the very least you have a duty and responsibility to ensure that your 'kill' is as clean and efficient as possible. I would think even a moron would agree with that –no?
Now, let's have a look at bow shooting. In order to be anywhere near competent enough to shoot animals I think it reasonable to expect the archer to be able to group ten arrows consecutively within a 24mm circle at a distance of 30 metre – and to be able to do this time after time after time.
Now, depending on what sort of bow you use, you could easily be pulling a draw weight of 40lb plus. It is not possible to sustain this level of static weight for more than a few seconds without affecting the accuracy of the aim. Difficult enough on a static target, let alone a moving one.
So, now let's have a look at the things that can and frequently do go wrong. The archer can have a poor loose, to happens to all of us occasionally, the arrow could be miss-knocked, or an un-noticed broken or faulty knock could be used the knocking point on the string could slip, I have even known archers knock an arrow below the point instead of above it by mistake. The arrow could lose a fletch or be incorrectly fletched, or be knocked upside down. Are you aware of just how an arrow flies as it leaves the bow? The knock is trying to overtake the pile throughout the length of its flight making it inherently unstable. Even a slight side wind affects the flight, much more so than a bullet.
No, archery is not the way to shoot animals. If you must do it, use a high power rifle.