Thinking in reasoning language models (RLMs) has been subject to debate on whether it resolves or amplifies bias. Prior works have shown competing conclusions in both directions. Using a within-model thinking-vs.-non-thinking ablation across QwQ-32B, DeepSeek-R1-Distill-Qwen-32B, and Qwen3-32B on three high-stakes decision tasks (Adult, COMPAS, Credit), we show that thinking has an asymmetric dual effect on counterfactual fairness: it both resolves counterfactual flips produced by the non-thinking baseline and creates new flips at near-saturating model confidence. In all nine (model, dataset) combinations, the created flips outnumber the resolved flips by roughly 5×. To explain the effect, we treat the thinking trace itself as a measurable site of fairness change and study it through two dynamic instruments: 1) We propose Counterfactual Depth Probability Gap (CDPG) to track bias evolution along thinking depth, and observe that bias propagates and amplifies with thinking. 2) We also formulate Bias Transition Matrices (BTM) to show how predictions of counterfactual pairs change from non-thinking to thinking, and find that the asymmetric dual effect originates in the pair-state joint transition.