Understanding mechanisms of resistance to antiviral inhibitors can reveal nuanced features of targeted viral mechanisms and, in turn, lead to improved strategies for inhibitor design. Arbidol is a broad-spectrum antiviral which binds to and prevents the fusion-associated conformational changes in the trimeric influenza hemagglutinin (HA). The rate-limiting step during HA-mediated membrane fusion is the release of the hydrophobic fusion peptides from a conserved pocket on HA. Here, we investigated how destabilizing or stabilizing mutations in or near the fusion peptide affect viral sensitivity to Arbidol. The degree of sensitivity was proportional to the extent of fusion peptide stability on the pre-fusion HA: stabilized mutants were more sensitive, and destabilized ones resistant to Arbidol. Single-virion membrane fusion experiments for representative Wild Type and mutant viruses demonstrated that resistance is a direct consequence of fusion-peptide destabilization not dependent on reduced Arbidol binding to HA at neutral pH. Our results support the model whereby the probability of individual HAs extending to engage the target membrane is determined by the composite of two critical forces: a "tug" on the fusion peptide by the extension of the central coiled-coil on HA, and the key interactions stabilizing fusion peptide in the pre-fusion pocket. Arbidol increases the free-energy penalty for coiled-coil extension, but destabilizing mutations decrease the free-energy cost for fusion peptide release, accounting for the observed resistance. Our findings have broad implications for fusion-inhibitor design, viral mechanisms of resistance, and our basic understanding of HA-mediated membrane fusion.