This paper demonstrates that the equivalence principle — the cornerstone of General Relativity stating that gravity and acceleration are locally indistinguishable — is routinely illustrated in textbooks and popular science using extended objects such as balls on strings. Through elementary reasoning and standard mathematical tools, the paper shows that gravitational time dilation and acceleration-induced time dilation produce opposite clock rate orderings across the top and bottom of any finite-sized object. The equivalence principle holds rigorously only in the point-particle limit, a qualification that standard pedagogical treatments systematically omit. The paper argues this constitutes a significant conceptual error in the common presentation of General Relativity and recommends that future treatments make the restriction to the infinitesimal limit explicit.