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Generalized global symmetries are present in theories of particle physics, and understanding their structure can give insight into these theories and UV completions thereof. We will identify noninvertible chiral symmetries in certain flavorful Z' extensions of the Standard Model, and our understanding of generalized symmetry breaking will lead us to short-distance theories of gauged non-Abelian flavor where nonperturbative effects can resolve important naturalness questions. For the leptons we will find naturally exponentially small Dirac neutrino masses, and in the quark sector we will construct a massless down-type quarks solution to strong CP in color-flavor unification. Intriguingly, the fact that we have three generations of fermions plays a crucial role in the existence of these noninvertible symmetries.