Legal case matching, which automatically constructs a model to estimate the similarities between the source and target cases, has played an essential role in intelligent legal systems. Semantic text matching models have been applied to the task where the source and target legal cases are considered as long-form text documents. These general-purpose matching models make the predictions solely based on the texts in the legal cases, overlooking the essential role of the law articles in legal case matching. In the real world, the matching results (e.g., relevance labels) are dramatically affected by the law articles because the contents and the judgments of a legal case are radically formed on the basis of law. From the causal sense, a matching decision is affected by the mediation effect from the cited law articles by the legal cases, and the direct effect of the key circumstances (e.g., detailed fact descriptions) in the legal cases. In light of the observation, this paper proposes a model-agnostic causal learning framework called Law-Match, under which the legal case matching models are learned by respecting the corresponding law articles. Given a pair of legal cases and the related law articles, Law-Match considers the embeddings of the law articles as instrumental variables (IVs), and the embeddings of legal cases as treatments. Using IV regression, the treatments can be decomposed into law-related and law-unrelated parts, respectively reflecting the mediation and direct effects. These two parts are then combined with different weights to collectively support the final matching prediction. We show that the framework is model-agnostic, and a number of legal case matching models can be applied as the underlying models. Comprehensive experiments show that Law-Match can outperform state-of-the-art baselines on three public datasets.