How can I convince my instructor to allow me to self-study?
It may be that you just have to comply with the instructor's wishes and do what is asked. Words are probably not going to convince them.
But, if you really want to convince them that you know the material, ask them to give you an exam, perhaps an oral exam, on the required material. If you do well, then they may be convinced. But if not, then you have the information you need that you really aren't ready.
An oral exam need only take 10 or 15 minutes, actually. Either you struggle or you excel. It can become obvious quickly which &quot;bin&quot; you fall in to.