If the source of the reported $3.5$ keV x-ray line is a sterile neutrino, comprising an $\mathcal{O}(1)$ fraction of the dark matter (DM), then it exhibits the property that its mass times mixing angle is $∼ \mbox{few} \times 10^{-2}$ eV, a plausible mass scale for the active neutrinos. This property is a common feature of Dirac neutrino mixing. We present a framework that dynamically produces light active and keV sterile Dirac neutrinos, with appropriate mixing angles to be the x-ray line source. The central idea is that the right-handed active neutrino is a composite state, while elementary sterile neutrinos gain keV masses similarly to the quarks in extended Technicolor. The entire framework is fixed by just two dynamical scales and may automatically exhibit a warm dark matter (WDM) production mechanism -- dilution of thermal relics from late decays of a heavy composite neutrino -- such that the keV neutrinos may comprise an $\mathcal{O}(1)$ fraction of the DM. In this framework, the WDM is typically quite cool and within structure formation bounds, with temperature $∼ \mbox{few}\times 10^{-2}~T_ν$ and free-streaming length $∼$ few kpc. A toy model that exhibits the central features of the framework is also presented. ; Comment: 9 pages, fig 2 added, published version