Well not the we have an opossum problem here in aus, but I'm on the don't kill it side.
I'm very much an animal girl and can't kill anything. I feel horrible if I so much as accidentally step on a tiny bug! I believe that every organism on earth has its place and as much right to be here as we do. They were here well before we were, and we have come in, invaded there space and decide because they annoy us we'll just kill them.
Humans have wiped out a HUGE 1/3 of the worlds animal kingdom. Now I really think that is atrocious and I feel ashamed to be part of a species that has dominated the world in such a terrible manner.
I believe that an animal should not be killed unless for a compassionate reason or that they will be put to good use. I am on the verge of being a vegetarian, when I think about the animals being killed for my eating I feel sick, however on second thought, lions do it every day and such animals are being slaughtered for a good purpose, to allow us to eat.
It is the killing for fun, or 'just because' that I really hate. Unless there is absolutely no other option, you have removed all sources of attraction for an animal onto your property, I see no reason to kill it.
Everyone goes out killing as many sharks as they can when there is a shark attack. Chances are they don't even get the culprit shark anyway. We are in THEY'RE territory, and they are only doing what they know to do. Animals don't conciously come onto 'our' properties to cause trouble, they do so because they are simply looking after themselves.
Get rid of all temptation and most likely the problem will be resolved, the animal will head back out and find another source of food and shelter.
Sorry, I just don't like the merciless killing of animals when they have done nothing to deserve it. It's not their fault. We are so quick to kill an animal that 'annoys' us... but do the animals come back in force and try to kill as many humans as possible when we obliterate their homes, environments, sources of food and shelter, when we kill their families, wipe out entire populations even??
I think we should learn from them rather than kill them. The world would be a much happier place.