The three pillars of a persuasive argument are logos, pathos, and ethos. Any convincing argument about staying in school will address all three of these items.
Logos is the logical portion of your argument. It offers facts and statistics. Therefore, an argument about staying in school would need to provide facts and statistics about the benefits of not dropping out. How, for example, do the earnings of high school graduates compare to those of people who never completed high school? What is the difference in incarceration rates between high school dropouts and high school graduates: is it more likely you will end up in jail if you drop out of school? Establishing these kinds of concrete facts will help convince readers of the soundness of an argument.
Pathos is emotional appeal. Facts alone leave people cold. It may be true that a high school graduate makes 58% more than a drop-out over their lifetime, but what does this mean? Pathos tells a story that puts flesh and bones, so to speak, on the statistics. A convincing paper would tell the story of what happens to a particular high school graduate versus a particular person who dropped out. You would have to do some research to find these two stories.
Finally, a convincing argument has ethos, or credibility. This means that you use what are accepted as reliable sources. For example, you would use The New York Times as a source, rather than a highly biased newspaper. An argument with good ethos also presents the writer as a knowledgable person who should be believed. You establish this credibility by editing and proofreading your writing so it is not filled with errors, as well as by using good sources.
Without all of these elements, any persuasive paper will fall short.