What do you think of the following opinion?
Neither you nor he is right.
Not either you or he is right.
Either you or he is not right.
Both you and he are not right.
Examples 1, 3, and 4 are grammatical; example 2 is not. ("Not either" = "Neither")
Examples 1 and 4 both mean the same thing, i.e., that both individuals are wrong (although some may argue that the two statements have differing connotations or emphases).
Example 3 does not mean the same thing as 1 and 4, but instead posits that only one person is wrong instead of both.