Perhaps they are concerned about their ability to teach a teen. For more information, read my article Homeschooling Teens. Maybe they are simply unsure of how to teach you at home, after you've been in school. You might find the article Leaving School and Learning at Home helpful. Of course, many parents still have the false belief that homeschooled kids are not socialized. The Socialization Myth will help to dispel their fears.
Our How to Homeschool topic page offers many resources. Read and print out any of these articles that may help your parents gain a greater understanding of what homeschooling entails.
Perhaps you need to ask for a family meeting. Set aside a day and time when there will be no interruptions and everyone has time to relax and discuss this topic in a calm, non-confrontational manner. List the reasons why you'd like to homeschool, the situation(s) that led to this decision, and the many advantages homeschooling offers. Remind your parents that they have nothing to lose by letting you try homeschooling, and if it doesn't work, you can always return to school after a mutually agreed-upon trial period. If they have any questions they need answered, assure them that I will gladly help them.