With Joy and Sadness lost somewhere in the recesses of Riley’s mind, it’s up to Fear (Bill Hader), Disgust (Mindy Kaling), and Anger (Lewis Black) to run Headquarters in their absence. At one point, Fear gives up trying to salvage Riley’s emotional state, and attempts to quit, leaving Headquarters through the same tube that sucked up Joy and Sadness. But the tube rejects him and throws him back, prompting Disgust to note, “Emotions can’t quit, genius.”
The emotions can’t quit, but Joy and Sadness were very much removed from Headquarters, which was functionally identical to what Fear tried to do. This seems to suggest two things. The first is that, while emotions being accidentally ejected during an emotional struggle is something that can happen, an emotion can’t voluntarily self-eject. Our feelings might get messy and incomplete for any number of reasons, but we’re not allowed to choose ones to get rid of.
The second is that Fear can’t remove itself from our minds out of, well, fear. There’s an argument to be made that fear is the most primal of all human emotions — the base instinct to evade danger and keep oneself alive and healthy. We can block out our sadness, our anger, and even our joy, but fear is not something that can be suppressed; it’s always there to some degree, an omnipresent participant in decision-making processes.