We show that propensity score matching (PSM), an enormously popular method of preprocessing data for causal inference, often accomplishes the opposite of its intended goal -- increasing imbalance, inefficiency, model dependence, and bias. PSM supposedly makes it easier to find matches by projecting a large number of covariates to a scalar propensity score and applying a single model to produce an unbiased estimate. However, in observational analysis the data generation process is rarely known and so users typically try many models before choosing one to present. The weakness of PSM comes from its attempts to approximate a completely randomized experiment, rather than, as with other matching methods, a more efficient fully blocked randomized experiment. PSM is thus uniquely blind to the often large portion of imbalance that can be eliminated by approximating full blocking with other matching methods. Moreover, in data balanced enough to approximate complete randomization, either to begin with or after pruning some observations, PSM approximates random matching which, we show, increases imbalance even relative to the original data. Although these results suggest that researchers replace PSM with one of the other available methods when performing matching, propensity scores have many other productive uses.