You write a comparison essay when you have no option but to convince a reader to agree to your point of view with comparisons. This normally happens when readers have certain preconceived ideas about certain events or objects that are deep rooted. It then becomes very difficult to remove the notion with the help of examples unless you compare the idea with a more powerful and compelling idea that readers would find difficult to contradict.
When you write a comparative essay, you are making comparisons for the benefit of the reader. It becomes very important for you to do so with the intention of convincing a reader of the merits of your argument. This becomes possible when you draw a powerful comparison between two opposing viewpoints. You have to be careful here that viewpoints are common and well known to readers. Only then will they be able to relate to both points of view.