Question: Do I have to go to animation school to be an animator?
Answer: That answer really depends on you, your talent, and your determination. Animation schools can be extremely expensive, but they provide a structured environment where you learn not only the fundamentals of animation, but also valuable career guidelines. You can make contacts that will serve you well for the rest of your life before you've even really launched into your career, and many schools offer internship programs or job placement programs that make it easy to gain a foothold without having to claw through resumes, interviews, and extremely stiff competition. The down side, though, is that schools are restricted in what they can teach and what software they can provide by their annual budgets and licensing restrictions, so your school may or may not be on top of the latest animation techniques. If you choose to go to school, research your schools and find out what they teach, how often they update, and what their credentials are.
If you have the talent and drive, though, there are plenty of animation resources available through libraries, bookstores, the internet, and one-shot classes that will let you learn on your own and might even promote further creativity by letting you find your own way rather than following structured rules. By keeping your nose in everything, you may be able to stay on top of the latest developments in animation techniques and technology to turn yourself into a competitive force. You also have more of a chance to diversify, while animation school may force you to pick a single path and focus on it as part of your degree program. The work involved in learning on your own is much harder, but costs many thousands of dollars less. Teaching yourself requires more discipline; finding work on your own requires more determination and effort.
Both options have their benefits and detriments. It's up to you to decide which will work better for you.