I don't think anyone's anti intellectual, people use rhetoric to defend their ideas, to defend their ways, to justify what they've already done. If you used your intelligence and started to agree with people, no one would challenge you, you wouldn't run into anti-intellectual bias.
When you challenge people, or disagree with them, they're going to use rhetoric against you, and that often is portrayed as anti-intellectual. If they think you're a threat they'll attack you by any means possible