With respect, I believe the composition relationship is not as you describe it. You may be confusing the classifier with the instance. You are correct in asserting that destroying (not deleting - more later) the Car classifier doesn't destroy the Wheel classifier. However, at the instance level, if the wheel is attached to the car, it must be destroyed with the car (think "nuked")! However, the wheel may be detached from the car (and therefore no longer participates in the composition) then it survives.
This is the essential difference between composite aggregation (aka "Composition") and shared aggregation (aka "Aggregation"). Aggregation is like Team membership, you can destroy the team without destroying the players. Also, a player can be in more than one team at the same time whereas the wheel can only be on one car at a time. The other distinguishing mechanism for which type of "holonymy is in play".
As I said, I treat every day as a school day. Looks like I need to go back to class, or at least wake up properly before posting.
I'd love to understand the philosophical aspects of all this a whole lot better. For one thing, the subtle difference between 'delete' and 'destroy' which I had never really understood properly.
*Could* you say that the 'car/wheel' Relationship can be described as both Aggregation AND Composition when considering either classifiers or instances? i.e.
> Aggregation in that there is not really any such thing as a 'car', that's just what you end up with by collecting (aggregating) enough bits and pieces (including, but not limited to, Wheels) together and attaching them in the right order. But any one of those pieces (e.g. 'Wheel' or 'Chassis') can exist perfectly well on its own without having to be 'Part of a Car'
> Composition in that once you destroy an instance of a Car, all of its constituent Parts (e.g. its 'wheel' instances) are also considered destroyed
At one point I thought I understood these concepts but now I'm not so sure...
Also major apologies for hijacking the thread, happy to continue this privately unless it is useful to other people too?!