In the context of a prototypical New Keynesian model, this paper examines the theoretical interrelations between two tractable formulations of progressive taxation on labor income versus (i) the equilibrium degree of nominal-wage rigidity as well as (ii) the resulting volatilities of hours worked and output in response to a monetary shock. In sharp contrast to the traditional stabilization view, we analytically show that linearly progressive taxation always operates like an automatic destabilizer which leads to higher cyclical fluctuations within the macroeconomy. We also obtain the same business cycle destabilization result under continuously progressive taxation if the initial degree of tax progressivity is sufficiently low.