In the present hypothesis paper on paradoxes in preventive medicine, which also deals with the indocility of biological functions, the following issues will be addressed. First, a definition of salutogenesis will be given, providing the origin of this notion of health preservation and disease prevention. Then, four paradoxes of the biology of health will be discussed. The first deals with the biomarkers of aging. The second addresses the good and bad of the much praised antioxidants. The third details how the mammalian transporter of rapamycin pathway plays a discreet but fundamental role. The fourth explores the yin and yang effects of the secretory profile of senescent cells. In conclusion, the need for a new paradigm in preventive medicine will be proposed.