Yes that is correct. Traditional anti-intellectualism came out of the French Revolution and intellectual obsession with freedom and equality of mankind (along with its anti-religious support from intellectuals).
Criticism of intellectuals comes from their own arrogance, elitism, and snobbery towards their fellow man, their support of liberal economics and uncaring feeling towards those "lower" than them, their being soft on Communism, their disgust of God and religion, their lack of common sense and lack of understanding of how the real world works, their serious attitude, their privelaged life, etc.