The idea is intellect is based around the ability to process time in your mind. You concentrate energy in order to not just come up with forms, but to also transform forms and reflect about the formulation of those forms.
Empiricism, in contrast, is mentally lazy. It looks upon the outside world of forms rather than making an effort to come up with forms.
Now to be fair, all forms don't make sense. It's like the difference between engineering and architecture. Some forms follow rules, and others don't. Some forms are functional and other forms are aesthetic.
This is why we worry about not being empirical. We worry that a person's mind can be mistaken or biased towards certain forms. People have opinions, and those opinions can be confused. After all, human nature is subrational. It has both thoughts and feelings. The idea of empiricism, therefore, is to guarantee no exposure of thoughts to feelings since the external world is beyond the capability of the internal mind.
The problem here is the world does not exist upon a point of singularity. The forms somewhere are not the forms everywhere. As mortal creatures, we do not pervade the world either. Therefore, we have limits in how many forms we can observe.
In turn, there really is no such thing as "objective" observation because the objects we observe are only some of the forms out there in the world. Yes, some observations are more objective than others. Scientific observation is less wrong than anecdotes and traditions, but it's ultimately speaking just that - less wrong.
The question then becomes a matter of whether we can overcome that "less wrong" limit. Is there a way to be purely right without being less wrong?
This is what brings us back to the mind's ability to process time, and this is where self-discipline becomes important, but the problem afterwards is a matter of trusting another's self-discipline. Just because someone claims to be self-disciplined doesn't mean someone really is. People can lie, be anxious, and be mistaken. Again, we use empiricism to overcome these problems...
...except empiricism doesn't really overcome these problems because people can lie, be anxious, and be mistaken about what they observe as well. Evidence can be fabricated, and the ability to check fabrication is not unlimited. There comes a point where people are again expected to trust others as the less wrong observers because it becomes ridiculous to check their evidence as faulty any further.
Unfortunately, this eventually leads to subtle forms of manipulation which become bigger over time by playing with the cracks of less wrong faultiness. It's a classic "wag the dog" situation. As civilization develops throughout generations and centuries, these cracks become a new form of pragmatic tradition as well. They form precedents of bad habits, and refusing to go along with them gets treated as rocking the boat, being difficult, and making things too inconvenient to be bothered.
This... is where anti-intellectualism rears its ugly head because people who think about these problems get dismissed and never addressed ever again. Society treats them as whiners, complainers, and targets of opportunity. It treats those who address the cracks as those worried about falling through the cracks, and it can't be bothered acknowledging them, so they're told to deal with it...
...and as civilization grows more accustomed to these bad habits, these cracks eventually become fault lines which lead to earthquakes. They become problems in which those who complained about them are told, "Don't say 'I told you so!' " Anyone who acknowledges those problems gets treated as doubly arrogant. They're labeled as vain for preaching, and they're labeled as too powerless to make a difference.
We get told these cracks are inevitable and unavoidable, not because they really are from self-discipline, but because the society we live in has games which are too difficult to be navigated. Therefore, solving these problems endures a vicious cycle of abandonment. For no other reason than because the people are too paranoid of one another, these problems of addressing less-wrong knowledge do not get addressed...
...but of course, there's no evidence of this...
...because to get evidence would require access to people's conduct and minds which gets restricted against those who are suspected of using that evidence against those who have it.
Hence, anti-intellectualism is solidified. Literally, access to evidence is not given to those who deserve it to prove their points about the problem of less wrong observation.