It is better to take many small steps in the right direction than to make a great leap forward only to stumble backward — Old Chinese proverb
The core principle of Peterson's "Clean your room"-message comes from the Broken Windows Theory (proposed by James Q. Wilson and George
Kelling in 1982).
The broken window is a metaphor for chaotic neighborhoods, which are characterized by incivility, graffiti, questionable entertainment, and whatnot.
The theory is based on the research that showed a link between incivility within a community and subsequent occurrences of serious crime.
When people see a small disorder here and another there, and everywhere, then their brains will start receiving the signals that disorders are acceptable in that given neighborhood. Which will result in a negative behavior modification.
On the flip side, if all the small disorders are taken care of, then it will affect the brain positively, modifying the behavior for good.
In a nutshell, if you avoid taking care of the small stuff then you will never manage the big stuff. However, if you take care of the small stuff then the big stuff will take care of itself. That's the idea.