A good argumentative essay will also acknowledge and refute the counter-argument. In your essay you should acknowledge the point that some people make that core academic classes are a more valuable use of instruction time than "playing games." By doing this, you are showing your understanding of the whole issue, and showing the totality of your argument.
While I agree with the reasons given in posts two and three, remember that you will need to fully explore each reason in your essay. Each reason that you give will need sound support and factual evidence. You might try putting each reason into its own paragraph. If you have a lot of evidence on a particular point, you may need more than one paragraph. For instance, if you were talking decreasing the deficit by increasing PE as suggested in post two, you might want a paragraph to explain how PE makes people healthier and a separate paragraph to explain how this would decrease the deficit and insurance costs.
Remember that in order to persuade someone, you must convince them of each aspect of your point. Simply listing reasons is not enough to be persuasive. You must explore those reasons in depth.
There is much research on the benefits of physcial education in the schools. With the tremendous rise in obesity in children, many studies have been conducted on how having P.E. in school helps overweight children to lose weight. Other studies may reveal how physical activity helps to release tension and provide students with excess energy to expel some of this so that they will be calmer when they return to class.
So, if you have a virtual library in your high school, your resource center workers should be able to guide you in your endeavor. Using actual data is a sound support for your argument.
To effectively persuade someone, you need to know what that person's concerns or interests are. This is true of the physical education issue. For example, if someone is concerned with people's health, you should emphasize that. You should emphasize, for example, that Americans as a group are way overweight and you should argue that more PE would help with this.
If someone were interested in reducing the federal budget deficit, you should argue that PE can help save money by making people healthier. Healthy people will not need to have as much money spent on them because they won't get sick as much.
If someone is interested in how they will look, emphasize that. Talk about the benefits of PE for a person's physique and overall looks.
If you are writing a generic essay (rather than trying to convince a particular person) put all of these in there. Use all the reasons that you can think of.