Some people argue that the verb 'be', as a copula verb, cannot take an object, so 'I' is correct. It was used more in the past, but now is used by a residual group of pedants. The other argument says that 99.9% cannot be wrong and it's perfectly OK to say 'me'. I'm afraid there is no clear answer on this. There are two styles of grammar- prescripivist (telling people what to say) and Descriptivist (describing what people say), and this is a classic example of where they disagree.
I imagine your teacher is one of the prescriptivists and thinks 'it is I' is the only correct form. Fifty years ago they were writing letters to the Daily Telegraph decrying the plural of 'takeovers' because Latin told them that prepositions couldn't have a plural. They seem to have given up that fight. The vast majority of grammars accept that people say 'it's me'. Many professors, doctors and judges use it. A tiny minority claim that they are custodians of the truth and the correct form. The argument has bounced around for years.
Who's right? I'd say both forms are acceptable.
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