Why not inherit from List?

Question

When planning out my programs, I often start with a chain of thought like so:

A football team is just a list of football players. Therefore, I should

Answer 1

There are a lot excellent answers here, but I want to touch on something I didn't see mentioned: Object oriented design is about empowering objects.

You want to encapsulate all your rules, additional work and internal details inside an appropriate object. In this way other objects interacting with this one don't have to worry about it all. In fact, you want to go a step further and actively prevent other objects from bypassing these internals.

When you inherit from List, all other objects can see you as a List. They have direct access to the methods for adding and removing players. And you'll have lost your control; for example:

Suppose you want to differentiate when a player leaves by knowing whether they retired, resigned or were fired. You could implement a RemovePlayer method that takes an appropriate input enum. However, by inheriting from List, you would be unable to prevent direct access to Remove, RemoveAll and even Clear. As a result, you've actually disempowered your FootballTeam class.

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Additional thoughts on encapsulation... You raised the following concern:

It makes my code needlessly verbose. I must now call my_team.Players.Count instead of just my_team.Count.

You're correct, that would be needlessly verbose for all clients to use you team. However, that problem is very small in comparison to the fact that you've exposed List Players to all and sundry so they can fiddle with your team without your consent.

You go on to say:

It just plain doesn't make any sense. A football team doesn't "have" a list of players. It is the list of players. You don't say "John McFootballer has joined SomeTeam's players". You say "John has joined SomeTeam".

You're wrong about the first bit: Drop the word 'list', and it's actually obvious that a team does have players.
However, you hit the nail on the head with the second. You don't want clients calling ateam.Players.Add(...). You do want them calling ateam.AddPlayer(...). And your implemention would (possibly amongst other things) call Players.Add(...) internally.

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Hopefully you can see how important encapsulation is to the objective of empowering your objects. You want to allow each class to do its job well without fear of interference from other objects.