Interpretability research takes counterfactual theories of causality for granted. Most causal methods rely on counterfactual interventions to inputs or the activations of particular model components, followed by observations of the change in models' output logits or behaviors. While this yields more faithful evidence than correlational methods, counterfactuals nonetheless have key problems that bias our findings in specific and predictable ways. Specifically, (i) counterfactual theories do not effectively capture multiple independently sufficient causes of the same effect, which leads us to miss certain causes entirely; and (ii) counterfactual dependencies in neural networks are generally not transitive, which complicates methods for extracting and interpreting causal graphs from neural networks. We discuss the implications of these challenges for interpretability researchers and propose concrete suggestions for future work.