Should we hunt and trap wolves? I say no! Wolves are just like stray dogs, we love dogs so we should keep it that way. I agree wolves can cause damage to our livestock and more, should we fix that. I am sure that we can help stop wolves hunting our livestock without trapping them.
We should hunt and trap wolves because if we don't, the big game will die out. We have to keep the animals in check here, we don't want to have any more extinct species on our hands, do we? If we let the wolves keep reproducing, then they will eat all the big game, and then starve.
If we kill our wolves or trap them we wont have any to help kill and lower the elk and deer population. I agree that every now and then the wolf population can get out of hand, but we can change that without having to kill them. We could simply start raising baby wolves and selectively breed them. Although we also may move wolves a habitat that does not pursue their needs so they may evolve into a new gene that does not produce as much or eat our elk and livestock.
The wolves hurt our livestock and, rarely, kill us. Some wolves don't go for elk or deer, they go for cattle. Then the person whom owns the cattle loses money and possibly their best cow. We don't need wolves to make the big game population go down, we have hunters for that.