We propose a fundamental challenge to the feasibility of moral progress: most extant theories of progress, we will argue, assume an unrealistic level of cognitive control people must have over their moral judgments for moral progress to occur. Moral progress depends at least in part on the possibility of individual people improving their moral cognition to eliminate the pernicious influence of various epistemically defective biases and other distorting factors. Since the degree of control people can exert over their moral cognition tends to be significantly overestimated, the prospects of moral progress face a formidable problem, the force of which has thus far been underappreciated. In the paper, we will provide both conceptual and empirical arguments for this thesis, and explain its most important implications.