We study text-based image editing (TBIE) of a single image by counterfactual inference because it is an elegant formulation to precisely address the requirement: the edited image should retain the fidelity of the original one. Through the lens of the formulation, we find that the crux of TBIE is that existing techniques hardly achieve a good trade-off between editability and fidelity, mainly due to the overfitting of the single-image fine-tuning. To this end, we propose a Doubly Abductive Counterfactual inference framework (DAC). We first parameterize an exogenous variable as a UNet LoRA, whose abduction can encode all the image details. Second, we abduct another exogenous variable parameterized by a text encoder LoRA, which recovers the lost editability caused by the overfitted first abduction. Thanks to the second abduction, which exclusively encodes the visual transition from post-edit to pre-edit, its inversion---subtracting the LoRA---effectively reverts pre-edit back to post-edit, thereby accomplishing the edit. Through extensive experiments, our DAC achieves a good trade-off between editability and fidelity. Thus, we can support a wide spectrum of user editing intents, including addition, removal, manipulation, replacement, style transfer, and facial change, which are extensively validated in both qualitative and quantitative evaluations.