If your question is do you necessarily need to stay in school to be able to eventually get the job that you want, then the answer is no. You can try to find a better way. But when employers out there post up a job, and they have 5 people apply with no professional experience, and 2 of them have a college degree, the people with the degree are more likely to get an interview. That's my experience anyway. The reality is with computer science, you only learn so much in college; everything else you are going to have to learn on your own. Technology changes very quickly, you might be learning one language in school today, and you might never need it throughout your career. Conversely, you will learn a lot of new languages on your own and after school, that you might use in a job, but won't even be touched in school.
My suggestion is to stay in school. While you're there, see about applying for an internship, or search craigslist for a junior web developer position somewhere. Graduate with a degree, and experience and go into your first job with a leg up on your competition. Good Luck!