A discovery of the flavor violating decay h --> tau mu at the LHC would require extra sources of electroweak symmetry breaking (EWSB) beyond the Higgs in order to reconcile it with the bounds from tau --> mu gamma, barring fine-tuned cancellations. In fact, an h --> tau mu decay rate at a level indicated by the CMS measurement is easily realized if the muon and electron masses are due to a new source of EWSB, while the tau mass is due to the Higgs. We illustrate this with two examples: a two

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... gs doublet model, and a model in which the Higgs is partially composite, with EWSB triggered by a technicolor sector. The 1st and 2nd generation quark masses and CKM mixing can also be assigned to the new EWSB source. Large deviations in the flavor diagonal lepton and quark Higgs Yukawa couplings are generic. If the muon mass is due to a rank 1 mass matrix contribution, a novel Yukawa coupling sum rule holds, providing a precision test of our framework. Flavor violating quark and lepton (pseudo)scalar couplings combine to yield a sizable B_s --> tau mu decay rate, which could be O(100) times larger than the SM B_s --> mu mu decay rate.