Why do I have to list my sources when writing an essay for school? I understand that I need to for proof when writing a research paper, or if the essay is to be published, but don't see the reason when only my teacher is going to read it.

The entire process of writing includes knowing the correct way to list your sources. Your teacher is not looking for just the proof, as you put it, but is looking to ensure that you are equipped with the knowledge of the process.

So, you are not doing this for the teacher, you are doing it to show that you are familiar with the correct way to list these sources. Think of it as advance learning for when you want to write that big research paper - at least you will have already learned how.