CBSE 12th

Pros: Youll gets a lot more time to study for JEE. There will be minimal if any, requirements for attendance. You will probably have to go to school 1/2 days a week and on some weeks, not at all. Since you will not be bogged down by a daily school routine, you will be able to devote more time for JEE prep. This obviously means better preparation, better rank, a good branch in an old IIT.
But that was obvious. The cons are not obvious, however.
Cons: As of now, you believe (or have been led to believe) JEE is the ultimate goal in your life. Once you crack JEE, you will have succeeded in your quest. You'll realise that this is a ridiculous lie once you get in (if you get in). Life comprises more than a decent AIR in JEE. Everyone in an IIT has qualified, so what distinguishes those of us who are inside than (no one cares about your AIR after a week)?
There are certain qualities in life which are highly desirable in people. These qualities are rare and difficult to acquire and certainly don't come from a thorough technical education. It is on the basis of these qualities that the highest echelons are filled when all other parameters are the same. People respect and admire those who possess such skills. What I speak of are generally known as soft skills: communication skills, confidence, poise, leadership skills etc. These are only inculcated in a school. The more elite or prestigious the school, the more it focuses on these qualities. Lastly, just like IIT, your school also represents a brand. You will have to name your school in your resume and a no name school adds nothing to it.
Decision: If you are studying in a decent or worse school, I suggest quitting and enrolling in a dummy school. No one in the real world cares about those. If however, you study in an elite or even semi-elite school, I would ask you to consider not quitting. It is entirely possible to prepare for IIT despite studying in a school. However, you must be resourceful and be prepared to periodically bunk classes as and when needed, keeping your attendance just on the borderline.