• a challenging endeavor -- not like going out and shooting an animal in a zoo.
• Animals in the wild tend to get killed in ways that are way worse than being shot.  They starve in the winter (not all, but some).  They are hit by cars.  They are torn to pieces by predators.  So what's so bad about being shot?

An argument or persuasive essay can best be characterized as taking one side on a position and supporting it with evidence after giving a concession to the opposing view.  In this case, it appears as if your teacher wants you to be prepared to argue either side of this issue.  In the end, you are the one who must decide which arguments on either side are most important.  What I can do is offer some ideas for you to reflect on and add to based on your own views about whether or not hunting is, indeed, a "barbaric practice."

Hunting is a barbaric practice:

• Animals are capable of feeling pain and often suffer when they are shot or trapped
• Hunting for sport is wasteful and cruel
• Hunting has caused virtual or actual extinction of some species of animals
• Excessive and uncontrolled hunting can disrupt the ecosystem, causing all kinds of terrible ripple effects.

Hunting is not a barbaric practice:

• Animals are not human beings and are generally to be consumed by humans
• Overpopulation of any animal in environments disrupted by human habitation must be curtailed for betterment of both animals and humans
• Skilled hunters can kill animals virtually painlessly
• An imbalance in the ecosystem can be corrected by enhancing hunting practices
• Hunting provides food.

This isn't, by any means, a definitive list; and not all of these arguments can be tied directly to the idea of barbaric.  This list doesn't include such things as the hypocrisy of those who abhor hunting yet eat meat from cattle or hogs slaughtered just as cruelly (if not more so) by meat-packing plants. 

If you're still struggling, I'd suggest taking a look at both the PETA (People for the Ethical Treatment of Animals) and NRA (National Rifle Association) sites--which I've included links to, below-- to see what else each site has to say about hunting and whether or not it's a barbaric practice.

To answer this question, you will want to define "barbaric." You may decide to use the definition of "savagely cruel" or "exceedingly brutal." Now think about the topic from two perspectives. Those who believe hunting is barbaric or cruel may look at the issue from the perspective of the animals and may take a more emotional point of view. Those who don't think it's barbaric may take a more human-centered perspective and may try to be less emotional.

For example, someone who thinks hunting is barbaric may point out that young animals may be deprived of their mothers—this is a theme many people know of from movies like Bambi. Another cruel aspect of hunting is that often an animal is wounded but doesn't die immediately, leading to prolonged suffering for the animal. Those who find hunting barbaric may believe that it is cruel to gain pleasure from killing a beautiful living thing when you don't need to. Few people in America need to hunt for their food because farm-raised meats are so readily available in stores. 

Those who believe hunting is not cruel often point to the fact that hunting eliminates overpopulation of species. In some areas, population of deer and other game animals would increase to the point of causing starvation and disease among the wild animals if hunters weren't allowed to decrease the population. Not only that, but overpopulation of these animals creates a nuisance and danger for humans, as they ravage yards and cause auto accidents. Those in favor of hunting may point out that predators are a part of the natural cycle of life. Animals in the wild are killed by their predators. In many cases a gunshot can be a more humane way of killing an animal than an attack by other animals. Wild game is often a more healthful meat, so it benefits the people who consume it, which is better than the animals being lost to starvation and disease.

The topic can be argued from both sides.