This paper exposes what really happens when interactive failure theories for fiber-polymer composites are combined with progressive-failure theories to justify discarding the predicted first-ply failure prediction in favor of a subsequent last-ply failure prediction. The procedure is shown to be far from the rational scientific process it is customarily presumed to be, even without any precise definition of the analytical procedure that is normally defined only in the associated computer codes, the source codes for which are not usually available. The paper shows how, and why, measured lamina properties are changed to others that cannot possibly be measured, and the theories changed, too, with no notice to that effect. The paper contains both qualitative and quantitative illustrations of the unacceptability of these theories, along with unresolved paradoxes that have bedeviled this process from the very start, but which have yet to be addressed. The never-justified simplifying assumptions made at the very first step of these analyses are explained, and a strong case is made that only mechanistic failure models, with separate equations for failures in the fibers, the matrix, and at the interface can be relied upon. An analogy can be drawn with reinforced concrete structures, the structural analysis of which requires the separate properties of steel and concrete, which are the “constituents” of this particular composite of materials. This does not imply that fiber-polymer composites can be characterized only at the micromechanical level; just that characterizations at the traditional macromechanical level must not be simplified (homogenized) to the point that they fail to adequately represent the dominant phenomena. Even for truly homogeneous materials, each mode of failure is completely defined by a single material reference property, be it a strength, a fracture toughness, or a modulus. It is noted that a need for multiple reference strengths should imply the presence of multiple independent failure mechanisms, not that there are interactions between them. A very strong recommendation is made that both the teaching and use of interactive composite failure theories cease forthwith, because the only applicability that any of these theories might have is to truly homogeneous anisotropic solids like rolled metallic plates and extrusions. Despite the fact that one of them, the Tsai-Wu theory, is the most widely taught theory for composites, not one of the many interactive theories for homogeneous anisotropic solids has ever been shown to have any relevance to inherently heterogeneous fiber-polymer composites. Progress towards simple reliable analysis tools for this task, to reduce the level of expensive testing that would be needed for entirely empirical characterizations, will not be achieved as long as these obstacles continue to stand in the way.