Here's my most common argument:
In any object-oriented system, there are two parts to any class:
Its interface: the "public face" of the object. This is the set of capabilities it announces to the rest of the world. In a lot of languages, the set is well defined into a "class". Usually these are the method signatures of the object, though it varies a bit by language.
Its implementation: the "behind the scenes" work that the object does to satisfy its interface and provide functionality. This is typically the code and member data of the object.
One of the fundamental principles of OOP is that the implementation is encapsulated (ie:hidden) within the class; the only thing that outsiders should see is the interface.
When a subclass inherits from a subclass, it typically inherits both the implementation and the interface. This, in turn, means that you're forced to accept both as constraints on your class.
With aggregation, you get to choose either implementation or interface, or both -- but you're not forced into either. The functionality of an object is left up to the object itself. It can defer to other objects as it likes, but it's ultimately responsible for itself. In my experience, this leads to a more flexible system: one that's easier to modify.
So, whenever I'm developing object-oriented software, I almost always prefer aggregation over inheritance.
