We examine optimal taxation and social insurance with adverse selection in competitive insurance markets. In a previous literature, it has been shown that, with perfect insurance markets, social insurance improves welfare since it is able to redistribute without creating distortions. This result has been taken as robust to the introduction of adverse selection as this would only provide additional justifications for social insurance. We show, however, that adverse selection can weaken the case for social insurance compared to a situation with perfect markets. Whenever social insurance mitigates private underinsurance, it also causes welfare-reducing effects by decreasing precautionary labor supply and hence tax revenue. In addition, adverse selection may reduce the redistributive potential of social insurance. We illustrate our general results using different equilibrium concepts for the insurance market. Notably, we derive conditions under which a complete renunciation of social insurance is optimal and the government only relies on income taxation to achieve its redistributive objectives.