Laurence’s answer is a good one. There remains a difficulty in how such questions are expressed.
Either or statements can vary in their precise meaning. The word or is known as a disjunction - the opposite of a conjunction. Disjunctions ‘disjoin’ statements, where conjunctions join them.
The disjunction “A or B” can have two meanings. The first (known as an inclusive disjunction) allows that A, or B or both A and B may be true.
Would you like either milk or sugar in your coffee?
The second (known, obviously as an exclusive disjunction) allows only one of the two alternatives to be true, but not both
Is the US President Democrat or Republican?
An *either or *question involving an inclusive disjunction is not, therefore, a dichotomy. Only if such a question involves the exclusive type of disjunction can Laurence’s false dichotomy arise.
The reason for saying this is that it is not easy to phrase a disjunction so that it is absolutely clear which kind it is.
Possibly, a statement “either A or B” is more likely to be interpreted as exclusive than it would be without the word ‘either’. But that is not foolproof, as the ‘milk or sugar’ example illustrates.
To be completely certain, you would have to say something like
Which would you like in your coffee, milk or sugar?
Then we immediately see the question to be inept, presenting a false dichotomy.
Am I just being a pedant? No. The disjunction is among the least understood elements of the language. Because of that it is the easiest for politicians and others to exploit for the purpose of deception.