[ Both / Neither / Either ] of my parents is British.

Hi,
Could someone explain this question clearly:

Both / Neither / Either of my parents is British.

My book says the answer is Neither

I know both is wrong because the verb of our sentence is singular I mean “Both of my parents are British” is correct.

But I don’t understand why Either is wrong.

I guess both of them are possible I mean we can say

Neither of my parents is British

Either of my parents is British

You just would not say “Either of my parents is British.” - you would say “One of my parents is British.”

Note that you could say “I don’t think either of his parents is British.”, but either does not work in the above sentence.

thanx Luschen