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Because writing classes to be substitutably extended is damn hard and requires you to make accurate predictions of how future users will want to extend what you've written.
Sealing your class forces them to use composition, which is much more robust.
I want to give you this message from "Code Complete":
Inheritance - subclasses - tends to work against the primary technical imperative you have as a programmer, which is to manage complexity.For the sake of controlling complexity, you should maintain a heavy bias against inheritance.
@jjnguy
Another user may want to re-use your code by sub-classing your class. I don't see a reason to stop this.
If they want to use the functionality of my class they can achieve that with containment, and they will have much less brittle code as a result.
Composition seems to be often overlooked; all too often people want to jump on the inheritance bandwagon. They should not! Substitutability is difficult. Default to composition; you'll thank me in the long run.
From an object-oriented perspective, sealing a class clearly documents the author's intent without the need for comments. When I seal a class I am trying to say that this class was designed to encapsulate some specific piece of knowledge or some specific service. It was not meant to be enhanced or subclassed further.
This goes well with the Template Method design pattern. I have an interface that says "I perform this service." I then have a class that implements that interface. But, what if performing that service relies on context that the base class doesn't know about (and shouldn't know about)? What happens is that the base class provides virtual methods, which are either protected or private, and these virtual methods are the hooks for subclasses to provide the piece of information or action that the base class does not know and cannot know. Meanwhile, the base class can contain code that is common for all the child classes. These subclasses would be sealed because they are meant to accomplish that one and only one concrete implementation of the service.
Can you make the argument that these subclasses should be further subclassed to enhance them? I would say no because if that subclass couldn't get the job done in the first place then it should never have derived from the base class. If you don't like it then you have the original interface, go write your own implementation class.
Sealing these subclasses also discourages deep levels of inheritence, which works well for GUI frameworks but works poorly for business logic layers.