Here is explanation you can use.
The proximity principle: I believe the simple rule of thumb is that when we use “Either” or “Neither” in the sentence with 2 single subjects, the verb should be in singular form. e.g.  Neither John nor Paul wants to go to the party. Of course, not everyone buys this rule.

Here is the rule: When one of the subjects joined by or/nor is plural, the verb must be plural. The plural subject should be placed nearest the verb.

Neither the chairman nor the directors are present.

This is because both the nouns (chairman, directors) are of equal importance. “Or” and “nor” are choices, right? And choices should be of equal importance. The nearest subject, “directors” is plural, so the verb is plural.

Briefly put, in neither … nor constructions, the verb should always agree with the noun nearest it. Thus, “Neither the contractor nor his agent were available for comment” should be “was available for comment.” Since the noun nearest the verb (agent) is singular, the verb should be singular. However, when the noun nearest the verb is plural, the verb should also be plural: “Neither the President nor his advisers were available for comment.”
When neither is used on its own, without the nor, the verb should always be singular: “Neither of the men was ready;” “Neither of us is hungry.”

In short, more often than not a singular verb is called for but that singularity is by no means invariable. Try to remember that neither emphasizes the separateness of items. It doesn’t add them together, at least not grammatically.
Finally, note that a neither … or combination is always wrong, as here: “[The] movie mixes horror with science fiction to make something that is fun as neither one thing or the other” (New York Times). Make it nor. The following sentence makes the same error and the additional one of failing to provide a grammatical balance between the neither phrase and the nor phrase: “Borrowing which allows a country to live beyond its means serves neither the interests of the borrower or the financial community” (Times). Make it “serves the interests of neither the borrower nor the financial community.”