The critical thinking literature strongly emphasizes separating prior opinion from evidence evaluation. This would seem to put the critical thinking literature squarely on the side of recommending that people overcome myside bias—one of the most ubiquitous biases studied in cognitive psychology. But myside bias presents many theoretical and empirical puzzles. It is unrelated to intelligence and it is conceptually difficult to show that it is an irrational information processing tendency. Most perplexing is that actively open-minded thinking, a disposition virtually defined as the ability to process information in a balanced manner, also does not correlate significantly with myside bias. These concepts present continuing puzzles for the critical thinking literature.