From a layman's perspevtive I've never understood the existence of angular momentum as anything other than a mental model or abstraction. My intuition tells me that all momentum is only linear (except maybe at the fundamental particle level), and perceived rotation is really just a huge amount of linear interactions by individual particles that make up a larger object. This is similar to how a gas is not really a singular thing but really a bunch of particles bouncing against each other, but can still be described by ideal gas laws as if it were a singular object.
What is the flaw in my thinking?