Can copyright prevent claims of self-plagiarism?
First off:


  I don't believe you can self-plagiarize.


I'm afraid that it doesn't matter what you believe about the word or its definition. It is not the reuse itself that is considered here, but it matters that most other academics believe that unattributed reuse of one's own work is ethically incorrect. If you choose to do things that most others label "self-plagiarism," then sooner or later it will not go well for you.

Now, as for your idea about copyright: potentially you could in fact make yourself a pain for the faculty members who deal with you.  You don't even have to be right or sane about your argument, you just have to threaten to make a big legal stink.  You will then greatly complicate your professor's lives, but one way or another you will not prevail: most likely either you will lose the legal case or the university may simply decline to continue instructing you.