It's because you're using one verb to apply to both subjects. So you're making two statements: 'I am not going there' (correct) and 'He am not going there' (incorrect). 'Am' cannot go with 'he'.
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TicceWhen I is one of the two subjects connected by either/or or neither/nor, put it second and follow it with the singular verb am.It doesn't seem right to compare or and nor. The word nor isn't the negative of or, it's the negative of and. When you say
Example: Neither she nor I am going to the festival.