This essay opens with a question about what science teaching would look like in a world where categorical seams of human diversity were not probabilistic determinants of science learning. After revisiting Hewson and Hewson's description of an "appropriate conception of science teaching," I detail the ways in which the field of science education has advanced in the decades since that article's publication. Drawing upon Cohen's notion of teaching as an "impossible profession," I highlight how conceptions of science teaching compete with other popular models of teaching and learning science. Fenstermacher and Richardson's distinction between "successful teaching," and "good teaching" is then presented to demonstrate that even science teaching that is considered successful and good remains embedded in a constrained system where well-regarded classroom practices may still lead to accumulated negative consequences. The essay ends with a discussion of complexity and recursiveness in science teaching, an argument for science teaching that includes embedded understandings of that teaching and learning on the part of the students themselves, and suggestions for a revised conception of science teaching.