Elastomeric networks often rupture at stresses hundreds or thousands of times lower than the gigapascal strength of their covalent bonds. The usual intuition is to look for a crack, a weak bond, or an unusually short polymer strand. Recently published molecular dynamics simulations instead trace the provenance of this behavior to a network-level mechanism–rare network-spanning shortest paths that become nearly straight while most of the network remains entropically elastic. We develop a closed-form mechanistic theory that turns this physical picture into quantitative predictions. Starting from a constrained variational principle for the network energy, our theory shows how macroscopic strength emerges from the statistics of network connectivity. Specifically, we find that first scission is controlled by a few exceptional paths that exhaust their molecular slack, but the peak strength is set by how many such paths are forced to carry load together. This distinction explains why an elastomer can lose strength after breaking only a small fraction of its bonds, why early damage need not resemble a crack, and why the stress first rises and then falls as the network is stretched. Given a finite-chain force law and specified path-population parameters, the reduced theory estimates first scission and peak stress, and derives a criterion for how selective path removal changes the scatter of the surviving population. We sharpen the design principle that stronger elastomers should suppress the population of network-spanning bond paths with unusually few bonds, rather than focus only on strengthening individual bonds or changing average connectivity. Further, recent {} X-ray computed tomography observations have revealed that nominally homogeneous silicone rubbers can deform non-uniformly even under uniform imposed strain, with local volumetric strains varying on the order of ten percent over millimeter length scales. We ask whether this observation changes the conclusions of our theory and, if not, what new insights follow from accounting for it. \auditchange{For independent lognormal path and stretch disorder, the statistical mixture predicts a lower, broader high-tension peak, with its location unchanged when the median local stretch equals the imposed stretch. Together with independently determined path statistics, these signatures provide a route to estimating regional stretch heterogeneity.