From my personal experience, bad neighbors are people who have a lack of respect for their neighbors. May sound simplistic, but I think it's pretty profound. If you have respect for your neighbors, and they have respect for you, then no one is taking advantage of the other, no one feels put upon, and there are no problems. I have a bad neighbor. I'm sure he'd say that I'm a bad neighbor too, but I'm not. He has encroached on my property, trimmed brush that was on my side of the property line, and dumped waste on my property. This was after I lent him tools and gave him some fill for free. My reason for, I suppose you could say "wanting someone else to fix it", is because he is a serial offender. He does it constantly, no matter what I say to him, and he now no longer speaks to me. The next time he pulls one of his stunts, I can't really take the law into my own hands, I don't want it to escalate into an actual war, I just want it to stop. So I'll call the police, they'll talk to him, he'll continue to hate me, and I'll continue to treat him with the respect that he will then have been forced to treat me with. I 100% agree that we should try to resolve our own disputes, but sometimes we have to deal with people who don't have the same respect for others that is shown to them.
Unfortunately, in the deer scenario, if the owner was unwilling to let me take the deer, I'd have to abide by that, as the deer is technically on his property. Out of respect, I'd ask, and out of respect, I'd hope he'd let me take it.