We're glad to hear that you liked Mike's explanation :) Regarding your question, in order for the sentence to be grammatically correct, we need to maintain the negative when referring to both alternatives (i.e. X and Y). We want to say that it is not X and it is not Y. To correctly say this, we need two negative conjunctions, neither and nor. When neither alternative is possible, something is neither X nor Y. On the other hand, "or" is used when referring to positive alternatives: something is either X or Y.
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