Why as the level of a college course goes up, is the course generally more specific and more specialized?
I strongly dispute your assertion that knowledge of the more general subject is not needed for the more specific subjects.  To use your own example, general biology will include general cell anatomy and metabolism and probably some basics of evolution.  More specialized courses like anatomy and endocrinology will make no sense without these basics.

Even when a direct subject material connection is not obvious, in a well-designed set of courses there is often an important dependence in skills.  For example, in the mathematics classes that I took, there was not much direct connection in material between Analysis and some the higher-level subjects like Abstract Algebra and Topology that had it as a required prerequisite.  However, Analysis was the subject where students were expected to learn how to properly approach and formulate mathematical proofs, and the higher-level subjects assumed these skills.  Likewise, many engineering departments have a required "general engineering" subject for freshmen, which drums in the general philosophy of engineering through hands-on applications in various areas: even if an electrical engineer never uses a machine-shop again, the "engineering way of thinking" that they have learned will be critical to their success later on.

Returning, then, to your basic question: there's an awful lot of knowledge in the world, and much of it simply is very specialized.  General classes give the foundation required by many different specialized subjects, and so a well-designed curriculum tends to naturally form a "tree" structure that starts general and becomes more specialized as one progresses deeper into a subject.