Modern physical education appeared in Europe at the end of the eighteenth century. In this article, we trace the developmental process of “instruction theory” in European physical education studies and sports science from the end of the eighteenth century to the present in order to consider the relationship between the didactics of physical education and contemporary training science. Focusing on general theories of instruction, we examine the nature of science and make proposals for the restructuring of training science that could be useful in practice. These considerations revealed the following points: 1) In Europe, the theory of instruction in physical education differentiated into Didaktik (didactics), Methodik (methodology), and Bewegungslehre (movement theory) in the 1950s and 1960s. 2) In the end of the 1960s, “Trainingslehre” (theory of training in competitive sport) appeared in Eastern Europe. In the 1970s, the theory of training based on induction from practical experience became a scientific discipline, and was applied as a general theory to various fields such as physical education, recreational sport, and physical activity for health. As a result, the name was changed to “Trainingswissenschaft” (training science). In this way, training science began to incorporate the didactics of physical education. 3) When attempting to restructure training science as an interdisciplinary applied science, we face an insoluble aporia. That is, human movement as a subject of study is so complex that any natural scientific approach needs to be divided infinitely into sub-disciplines, making it more difficult to integrate as an interdisciplinary science. 4) In order to overcome this problem, it is necessary to derive a general theory from practice, rather than from principles of established science. We propose the term coaching science to describe this new theory.