The somatic mutation theory of carcinogenesis has been the dominant force driving cancer research during the 20th century. In brief, it proposes that successive DNA mutations in a single cell cause cancer (monoclonality). This theory places carcinogenesis at the cellular and subcellular hierarchical levels of biological complexity. Its basic premises are that (1) cancer is a defect of the control of cell proliferation and (2) the default state of metazoan cells is quiescence. These two premises have recently been contradicted by evidence. Supporters of the theory have dealt with these lacks of fit by incorporating ad hoc explanations similar to the use of epicycles in pre-Copernican astronomy. We propose the adoption of an alternative theory, the tissue organization field theory of carcinogenesis and neoplasia. Its basic premises are that (1) proliferation is the default state of all cells and (2) carcinogenesis and neoplasia are defects of tissue architecture. Carcinogens would act initially by disrupting the normal interactions that take place among cells in the parenchyma and stroma of an organ (the equivalent of the "morphogenetic fields" of developing organisms). Stroma appears as the primary target of carcinogens. Carcinogenesis and neoplasia occur entirely through emergent (supracellular) phenomena. Neoplastic cells may be reprogrammed to behave like "normal" cells within normal tissues. We argue that it is necessary to abandon the somatic mutation theory. Researchers will then become free to adopt alternative reliable premises to build a theory that explains carcinogenesis as another outcome, aberrant as it may be, of biological organization.