The thesis that LeGuin asserts in her short story is that the philosophy of utilitarianism is unethical. This philosophy argues that happiness comes to the society that adheres to the principle of finding "the greatest good for the greatest number."
LeGuin shows a society in which everybody else's happiness is dependent on the suffering of one innocent child. By forcing the reader to look at this one suffering child, he or she is filled with revulsion that such a thing could be allowed. We therefore join her in questioning the concept of the greatest good for the greatest number.
One way you could go would be to push back against LeGuin's thesis. Are there values in spreading out happiness as widely as possible, even if one person has to suffer for it? What good does it do for more people to be thrown into misery?
You might also look at how happiness is portrayed in the story. Is true happiness based on than more than material goods, brilliant festivals, and a physically beautiful place to live? Are the people in Omelas really happy? Perhaps you could argue that the people of Omelas are only happy in a shallow way. Perhaps LeGuin is offering a false choice. Maybe if the people of Omelas refused to torture one child, their festivals and beautiful surroundings and material well being would go away, but they would find that none of this mattered to begin with. Perhaps they would find a truer, deeper happiness through sacrificing for another (a tenet of many major religions).
All of these are ways to challenge LeGuin's thesis. If you were, say, to argue that the people of Omelas are not really happy, you would have to pull descriptions of happiness from the text and question whether this was true happiness. You would then have to go outside of the text and pull some definitions of happiness from other sources--or at least one other authoritative source, such as Seneca or Plato or Jesus. Then you could also question, using quotes from the text, whether people who are subconsciously aware of an innocent child suffering for their happiness are truly happy.
Whatever you do, be sure to back up you argument with quotes from the story.