Choose a topic that does not receive much attention in the media or that you do not hear much about and create an essay from that. Explain why you think it is relevant and important to consider. You can also explain why you think that particular issue has been neglected and in what ways the general public or your audience can strive to make that issue more important in society. Suggest how the issue can be dealt with and why the audience should care as well.
Controversial things are happening all the time in regular news. Flip on the news channel or pick up the paper and start hunting for a topic. When you find a story that you have strong feelings about one way or the other, you can use the topic of that story for your paper. Anything from political squabbles to white-collar crime can be used as a topic for an argumentative essay, just as long as there are two clear points of view.
Choose a topic that you feel strongly about that is frequently misrepresented in the news or in the common public. Prove that it deserves more criticism than it has received by explaining why it is important to the common public and why your audience should care about it. Choose a topic from history that the general public might not know the full story about and fill in the blanks by giving hard evidence that your readers cannot ignore.
Structure your argumentative standpoint so that is unique to the argument that you are proposing. For example, if you are arguing about immigration laws, discuss the historic formation and definition of immigration laws since the original conception of the Constitution. Making your structure unique to your argument will make it more relevant and interesting to your audience.