Do you think he's being fair?
No, he isn't really being fair with it, I think he should point out what is plagiarism and what isn't plagiarism.
Is it my right to have another chance?
Well, I'm kind of torn between this one, I think teachers have the right to say "No" for students to have another chance to re-do it and I also believe students have the right to re-do the essay to get a better grade.
Is it right for me to take matters into the prinicpal's hands?
Yeah, if you think it's completely unfair of him to do that, and not give you any proof to why he thinks or knows it's plagiarism, I mean teachers shouldn't leave their students in the dark.
Is it the teacher's given right to look at my essay and state it as plagerism without proof?
Nope!