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Semi-supervised object detection has made significant progress with the development of mean teacher driven self-training. Despite the promising results, the label mismatch problem is not yet fully explored in the previous works, leading to severe confirmation bias during self-training. In this paper, we delve into this problem and propose a simple yet effective LabelMatch framework from two different yet complementary perspectives, i.e., distribution-level and instance-level. For the former one, it is reasonable to approximate the class distribution of the unlabeled data from that of the labeled data according to Monte Carlo Sampling. Guided by this weakly supervision cue, we introduce a re-distribution mean teacher, which leverages adaptive label-distribution-aware confidence thresholds to generate unbiased pseudo labels to drive student learning. For the latter one, there exists an overlooked label assignment ambiguity problem across teacher-student models. To remedy this issue, we present a novel label assignment mechanism for self-training framework, namely proposal self-assignment, which injects the proposals from student into teacher and generates accurate pseudo labels to match each proposal in the student model accordingly. Experiments on both MS-COCO and PASCAL-VOC datasets demonstrate the considerable superiority of our proposed framework to other state-of-the-arts. Code will be available at https://github.com/hikvision-research/SSOD.