Choosing an environmental issue lends itself well to an argumentative essay, because you can use scientific research to back up your debate. Such topics as recycling, pollution and the destruction of the ozone layer have been thoroughly researched and written about, so you can use books and articles to back up your arguments.
Statistics and studies exist for social issues, making such issues an appropriate topic for an argumentative essay. Topics such as the impact of women in the workplace or how unmarried parents support their families can be written about easily, because decades of studies are available to back up an opinion.
The economy provides several topics that would work well in an argumentative essay. You can make an argument for how an economy thrives or fails, or you could argue the pros and cons of economies outside the United States, asserting which countries you feel have the best economic models.
A number of watershed moments in U.S. legal history can be debated in an argumentative essay. Topics such as the civil rights movement, women's suffrage and immigration issues have aspects that can be represented in an essay, and backed up with primary-source documents and legal rulings.