Is "either" used correctly in this case?

Question

Is the sentence below correct?

Either a desire for revenge or the protection of society cannot have been the only motive.

...and would the sentence below be a better alternative to the one above?

Neither a desire for revenge nor the protection of society could have been the only motive.

Edit: Below are the question and the accompanying choices.

Q32: Which of the following is the most effective way to combine these sentences?

A. Revenge cannot have been the only motive; protection cannot have been the only motive, either.

B. Either a desire for revenge or the protection of the society cannot have been the only motive.

C. The motive cannot have been the desire for revenge or the desire to protect society.

D. A desire for revenge cannot have been the only motive, but the motive cannot have been only protection, either.

Answer 1

Of those choices, B is arguably the best, but using “either” with negation can be ambiguous and should be avoided; this is why we have “neither”:

• Neither a desire for revenge nor protection of society could have been the only motive.