One of the motivations for anti-intellectualism is the appeal to "keep it simple." Simplification makes things easier to understand, but at a cost. Something is lost in translation.
While teaching is about helping people to understand, and simplification is a necessary step along the way, real understanding requires coming to terms with increasing levels of complexity. Education is a process of initiation into more complex truths.
The process of clarification requires stripping complex concepts down, but then building them back up again, layer by layer. Teachers can show their students how to do this, but students need to learn to repeat this on their own over and over again until they themselves become able to see the simple in the complex, and the complex in the simple.