The cosmic microwave background radiation is routinely cited as evidence for a hot Big Bang. Its isotropy harmonizes with the cosmological principle. However, in prototypical Big Bang models, all matter originates from a primeval fireball that also emits the light that is redshifted into these microwaves. Since light escapes from its source faster than matter can move, it would need to return for it to still be visible to material observers, but the universe is considered ‘flat’ and non-reflective. This prevents us from observing the redshifted glow of the primeval fireball. Like its observability, its homogeneity would also be transient. This is concealed by considering the light to expand with the ‘Hubble flow’ while disregarding that it escapes at c. This blunder reflects the practice of treating model universes in General Relativity as filled with a spatially homogeneous fluid. For radiation, this becomes inappropriate when it is no longer scattered. What we actually observe remains unexplained. Moreover, the calculation of line-of-sight distances allows an expanding view into a large pre-existing universe. For other aspects, the universe is assumed to have been smaller before. This creates contradictions such as between the observed source of the cosmic microwaves and their much smaller and closer assumed emitting source. The criticism expressed here goes against the ‘hard core’ of an established research program. Those cores are treated as inviolable, which blocks fundamental progress. Such blockage can persist for generations even if the theory that is promulgated as the best we have is actually irrational.