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The role of instability in the growth of a 2D, temporally evolving, `turbulent' free shear layer is analyzed using vortex-gas simulations that condense all dynamics into the kinematics of the Biot-Savart relation. The initial evolution of perturbations in a constant-vorticity layer is found to be in accurate agreement with the linear stability theory of Rayleigh. There is then a stage of non-universal evolution of coherent structures that is closely approximated not by Rayleigh stability theory, but by the Karman-Rubach-Lamb linear instability of monopoles, until the neighboring coherent structures merge. After several mergers, the layer evolves eventually to a self-preserving reverse cascade, characterized by a universal spread rate found by Suryanarayanan et al. (Phys.Rev.E 89, 013009, 2014) and a universal value of the ratio of dominant spacing of structures ($Λ_f$) to the layer thickness ($δ_ω$). In this universal, self-preserving state, the local amplification of perturbation amplitudes is accurately predicted by Rayleigh theory for the locally existing `base' flow. The model of Morris et al. (Proc.Roy.Soc. A 431, 219-243, 1990.), which computes the growth of the layer by balancing the energy lost by the mean flow with the energy gain of the perturbation modes (computed from an application of Rayleigh theory), is shown, however, to provide a non-universal asymptotic state with initial condition dependent spread-rate and spectra. The reason is that the predictions of the Rayleigh instability, for a flow regime with coherent structures, are valid only at the special value of $Λ_f/δ_ω$ achieved in the universal self-preserving state.