Table-based fact verification aims to verify whether a statement sentence is trusted or fake. Most existing methods rely on graph feature or data augmentation but fail to investigate evidence correlation between the statement and table effectively. In this paper, we propose a self-Labeled Keypoint Alignment model, named LKA, to explore the correlation between the two. Specifically, a dual-view alignment module based on the statement and table views is designed to discriminate the salient words through multiple interactions, where one regular and one adversarial alignment network cooperatively character the alignment discrepancy. Considering the interaction characteristic inherent in the alignment module, we introduce a novel mixture-of experts block to elaborately integrate the interacted information for supporting the alignment and final classification. Furthermore, a contrastive learning loss is utilized to learn the precise representation of the structure-involved words, encouraging the words closer to words with the same table attribute and farther from the words with the unrelated attribute. Experimental results on three widely-studied datasets show that our model can outperform the state-of-the-art baselines and capture interpretable evidence words.