Kantian universalization tests the maxim behind an action: the situation, action, and end that express the agent’s reason. One asks whether that maxim could be conceived and willed as a universal law. The test concerns rational consistency and willing, rather than a forecast that everyone will copy the behavior.
A maxim should describe the agent’s reason, including the relevant circumstance, proposed action, and end. Describing it as an arbitrary exception for one named individual avoids the moral issue rather than answering it. The universal-law test then asks about general authorization of that principle. The argument differs from predicting how many people would copy the behavior: it examines the coherence of a practice and of rational willing under the proposed rule.