A Fermi arc is a disconnected segment of a Fermi surface observed in the pseudogap phase of cuprate superconductors. This simple description belies the fundamental inconsistency in the physics of Fermi arcs, specifically that such segments violate the topological integrity of the band. Efforts to resolve this contradiction of experiment and theory have focused on connecting the ends of the Fermi arc back on itself to form a pocket, with limited and controversial success. Instead, we find the Fermi arc, while composed of real spectral weight, lacks the quasiparticles to be a true Fermi surface. To reach this conclusion we developed a new photoemission-based technique that directly probes the interplay of pair-forming and pair-breaking processes with unprecedented precision. We find the spectral weight composing the Fermi arc is shifted from the gap edge to the Fermi energy by pair-breaking processes. While real, this weight does not form a true Fermi surface, because the quasiparticles, though significantly broadened, remain at the gap edge. This result requires the existence of a finite gap above TC which we find is not correlated with the traditional T* for the pseudogap in the cuprates but the intermediate temperature scale TPair found by Nernst and diamagnetism experiments that are extremely sensitive to pair formation. Consequently, we have spectroscopic evidence for pre-formed pairs in the cuprates. We argue that the confusion over the nature of the pseudogap arises from the existence of two distinct pseudogaps: an ordered state that forms at T* and is primarily limited to the anti-node and a pre-pairing gap that forms at TPair and is most easily found in the near-nodal region.