Case in point, my boss at the moment does something I've noticed quite often in stupid people. As soon as the train of thought requires more than about 10 or 15 seconds of quiet thinking and analysis, he immediately changes the subject. He either changes the subject to something that (to my mind) is completely unrelated, or he makes some vague self-affirming statement.

On the one hand, this is annoying as fuck. On the other hand, if I look at it objectively, his brain is just wired that way. He doesn't have the capacity to break down an argument or situation to its atomic level, so his brain compensates by changing the subject and continuing the analysis, albeit on another topic.

It's really just another manifestation of the idea that our brains are constantly analysing things, but it just so happens that this manifestation is incredibly frustrating to anybody who enjoys getting to the bottom of and solving problems.

Have you ever noticed differences in the level of awareness different people display? (And, indeed, the same person from day-to-day.)

Some people call it mindfulness, awareness, self-awareness, introspection, analytical, etc.

People vary greatly in their conscious awareness of the world around and inside themselves. When OP states "very analytical", they are saying they feel like they're more aware than they perceive other people to be.*

* This has its own considerations.

Of course most people can do both, but often people are better at one or the other.

(Although usually, only people with analytical minds waste their time thinking about it.:)