The spectacularly wrong theory is not the dangerous one. It is refuted, abandoned, and remembered fondly as an anecdote. The dangerous theory is the one that is nearly right. Consider the pre-Copernican model of the heavens. It is routinely presented as an embarrassment, but this misrepresents the difficulty. Ptolemaic astronomy was not stupid; it was accurate. It predicted planetary positions to within a degree or two, which was better than most observations of the period could distinguish. Its epicycles were not superstition but curve-fitting, and curve-fitting works. That was precisely the problem. A model that fails obviously invites replacement. A model that fails subtly invites repair, and repair is intellectually cheaper than reconstruction. Each new epicycle was individually reasonable. The cumulative structure became indefensible, but no single step in its assembly was a mistake anyone could point to. This pattern is not confined to antiquity. It recurs whenever a framework is productive enough to keep generating results while being wrong in its foundations. Practitioners are not being stubborn; they are being locally rational. Abandoning a working framework costs a career, and the replacement, in its early years, always performs worse than the incumbent. Copernicus was less accurate than Ptolemy for decades. The uncomfortable conclusion is that the standard heroic narrative inverts the actual difficulty. We tell students that science advances by testing predictions against evidence, and it does, but this understates how long a nearly-right theory can absorb disconfirming evidence without breaking. Anomalies do not announce themselves as anomalies. They arrive as measurement error, as special cases, as problems for future work. What eventually breaks such a framework is rarely a single decisive experiment. It is usually the accumulated cost of maintenance becoming visible to a generation that did not build it, and therefore has no investment in its survival. There is no method for recognising this from the inside. The best that can be said is that a field which finds itself repeatedly explaining why its exceptions are exceptional should probably be nervous, and that the discomfort of that suspicion is not a flaw in the scientist but the ordinary texture of doing the work.