Reforming America’s health-insurance system was never going to be an easy task, given people’s natural aversion to change (not to mention Republicans’ aversion to doing anything that might help Barack Obama). But what’s made the task even more difficult is that American politicians—as well as American voters—have a confused, and often contradictory, set of beliefs about how health insurance should work. The wayward, patchwork plan that we seem likely to end up with is probably a good reflection of the wayward, patchwork opinions that most legislators have on the subject.

Consider the Genetic Information Nondiscrimination Act, which went into effect in November. The law prohibits health insurers from using genetic information to set rates or deny...