Yes humans are superior to animals and do have some right to hunt them. Hunting is not just done to kill animals. It also helps to control the animal population and for some gives people something to eat. We have a right to hunt animals as long as we are following our laws.
I believe humans are superior to animals. I think the best way to illustrate this, is with the food chain. Animals eat other animals, some animals eat plants, others eat both. We are at the top and generally we eat both. I think it is human nature to hunt, given the fact that we wouldn't be here if our ancestor's had not hunted.
I do believe that humans are superior to animals, but in the end humans are animals themselves. I have personally never believed in hunting for sport, because an animal is so vulnarable and helpless when facing a gun. There is something just so wrong to me about hiding and shooting down an animal who can't really defend themselves.
Since Homosapiens came to rule the earth, it has been natural to hunt. While hunting extremes, such as hunting but not using the meat, can be overdone, the majority of hunters, in the United States, do it responsibly. Currently the curve is that there is overpopulation of some deer and quail, so if they are hunted responsibly, it is ok.
Humans are different than animals but in the total scheme of things not superior because all have a right to exist. Hunting for food is one thing, but there is no justification for sport hunting. It is an immoral thing to do and we have been given no authority to do that.
I don't believe that we have authority to hunt animals because we are superior. I don't believe that we are superior. We are just smarter in certain ways. I am vegetarian and dislike any hunting, but if a person hunts an animal for meat, then they are doing so to satisfy a biological impulse that they might have, just like other animals might.
Humans are animals just like any others, perhaps even lesser than animals for the selfish, ugly ability to be conscious of their own self and thinking this somehow puts them above others. Murder is murder, between human and human or human and animal. Hunting is a tradition rooted in self-preservation, there's no need for it in industrialized, modern society.