Semi-supervised learning (SSL) suffers from severe performance degradation when labeled and unlabeled data come from inconsistent data distributions. However, there is still a lack of sufficient theoretical guidance on how to alleviate this problem. In this paper, we propose a general theoretical framework that demonstrates how distribution discrepancies caused by pseudo-label predictions and target predictions can lead to severe generalization errors. Through theoretical analysis, we identify three main reasons why previous SSL algorithms cannot perform well with inconsistent distributions: coupling between the pseudo-label predictor and the target predictor, biased pseudo labels, and restricted sample weights. To address these challenges, we introduce a practical framework called Bidirectional Adaptation that can adapt to the distribution of unlabeled data for debiased pseudo-label prediction and to the target distribution for debiased target prediction, thereby mitigating these shortcomings. Extensive experimental results demonstrate the effectiveness of our proposed framework.