Logical reasoning is needed in a wide range of NLP tasks. Can a BERT model be trained end-to-end to solve logical reasoning problems presented in natural language? We attempt to answer this question in a confined problem space where there exists a set of parameters that perfectly simulates logical reasoning. We make observations that seem to contradict each other: BERT attains near-perfect accuracy on in-distribution test examples while failing to generalize to other data distributions over the exact same problem space. Our study provides an explanation for this paradox: instead of learning to emulate the correct reasoning function, BERT has, in fact, learned statistical features that inherently exist in logical reasoning problems. We also show that it is infeasible to jointly remove statistical features from data, illustrating the difficulty of learning to reason in general. Our result naturally extends to other neural models (e.g. T5) and unveils the fundamental difference between learning to reason and learning to achieve high performance on NLP benchmarks using statistical features.