Pedagogy for biology (genetics)
First, let me say that I share your feelings about the way biology is typically taught (i.e. as a collection of facts). I believe this will change in the not-so-far future.

Now, some historical perspective:

Biology was, for a long time, a field of science which was mostly concerned with making observations and collecting data. Even though people were interested in the underlying mechanisms, they were often very difficult to understand in a principled way. This is mostly because biological systems are complex systems, in the sense that very complicated system-level behavior (often referred to as phenotype, e.g. mitosis) emerges from interactions between many (e.g. tens of thousands) different types of elements. This makes these systems very difficult to understand by only looking at a handful of elements.

As our ability to collect and analyze data has improved due to technological advances (computing power and high-throughput biological experiments), along with a better ability to perform genetic perturbations (e.g. genetic engineering), biology is becoming more and more quantitative. This has given rise to new fields such as computational biology and systems biology. Still, this approach to biology is very new, and so most biology courses (and books) are taught in the "classic" way. In many cases, we simply do not understand yet the logic or mechanisms underlying certain phenomena in a quantitative way.

Since courses that teach biology from the systems biology / physics / mathematical perspective at an introductory level are still quite rare, I suggest starting with a book (for example, "Physical Biology of the Cell" by Phillips et al. is one such example of teaching biology from a physics perspective; SPOILER: statistical thermodynamics are very useful).