Actually I choose better partners. I would rather roll with an upper belt than roll with a stubborn white belt.
I actually like those who would be considered "white belt" They are often wild and panic a great deal. In striking this means that I actually have to be better with my defense. With upper skilled level practitioners, I benefit from their ability to control their strikes. With a beginner, I better be on my guard and keep my defense ready for something out of the blue and unorthodox.
Grappling is the same with me. Those who are more skilled than me are more conservative. They put in just enough to control me. The guys that are new to wrestling aren't the same. They go full on force me to go at a faster pace and do a lot of unexpected things that aren't the best options for them to take but are still things that catch me off guard.
In other words, you find comfort in the control of the higher belts, but aren't so comfortable with the raw power that white belts put out. No matter how dumb squeezing is for a plan. A white belt will put their all into making that plan work. They rather prevent you from being able to use your skill sets than to try to work their own in a way that they feel would make them pay big for the mistakes.
In short their strategy is to shut you down and to prevent you from using your skills. This is the same strategy that I speak of when dealing with grapplers. A grappler can only use their grappling skills if they can get a hold of me. BJJ can only have a big advantage if they put me on the ground. So, my strategy is to prevent them from being able to use their skill set.
This sounds like the same situation you are in. You can't work your skills because the white belt is shutting you down. He's not advancing and going offensive, but he probably doesn't care. I would be curious to know if his "good day" is any day where he can shut someone down and make it difficult to use their technique.