If a person is part of a team, and a team is part of a club, it doesn't make sense to say that a club is part of a person. Figure 8 Illegal UML model. Aggregations should not form a cycle. But avoidance of such a bizarre occurrence doesn't seem to be a compelling reason to add aggregation to ORM's formal notation. There are plenty of associations between Club and Person that do make sense, and plenty that don't.
Composition does add some important semantics to shared aggregation.
To begin with, it requires that each part belongs to at most one whole at a time. In this example, the ORM model explicitly includes an acyclic constraint. For example, Finger belongs to Hand is an aggregation, but Ring belongs to Finger is not. There is some disagreement among authors about what should be included on this list. My own viewpoint is that for conceptual modeling purposes, agonizing over such distinctions doesn't seem to be worth the trouble.