Why can't I have abstract static methods in C#?

Static methods are not instantiated as such, they're just available without an object reference.

A call to a static method is done through the class name, not through an object reference, and the Intermediate Language (IL) code to call it will call the abstract method through the name of the class that defined it, not necessarily the name of the class you used.

Let me show an example.

With the following code:

public class A
{
    public static void Test()
    {
    }
}

public class B : A
{
}

If you call B.Test, like this:

class Program
{
    static void Main(string[] args)
    {
        B.Test();
    }
}

Then the actual code inside the Main method is as follows:

.entrypoint
.maxstack 8
L0000: nop 
L0001: call void ConsoleApplication1.A::Test()
L0006: nop 
L0007: ret 

As you can see, the call is made to A.Test, because it was the A class that defined it, and not to B.Test, even though you can write the code that way.

If you had class types, like in Delphi, where you can make a variable referring to a type and not an object, you would have more use for virtual and thus abstract static methods (and also constructors), but they aren't available and thus static calls are non-virtual in .NET.

I realize that the IL designers could allow the code to be compiled to call B.Test, and resolve the call at runtime, but it still wouldn't be virtual, as you would still have to write some kind of class name there.

Virtual methods, and thus abstract ones, are only useful when you're using a variable which, at runtime, can contain many different types of objects, and you thus want to call the right method for the current object you have in the variable. With static methods you need to go through a class name anyway, so the exact method to call is known at compile time because it can't and won't change.

Thus, virtual/abstract static methods are not available in .NET.

Static methods cannot be inherited or overridden, and that is why they can't be abstract. Since static methods are defined on the type, not the instance, of a class, they must be called explicitly on that type. So when you want to call a method on a child class, you need to use its name to call it. This makes inheritance irrelevant.

Assume you could, for a moment, inherit static methods. Imagine this scenario:

public static class Base
{
    public static virtual int GetNumber() { return 5; }
}

public static class Child1 : Base
{
    public static override int GetNumber() { return 1; }
}

public static class Child2 : Base
{
    public static override int GetNumber() { return 2; }
}

If you call Base.GetNumber(), which method would be called? Which value returned? It's pretty easy to see that without creating instances of objects, inheritance is rather hard. Abstract methods without inheritance are just methods that don't have a body, so can't be called.

Another respondent (McDowell) said that polymorphism only works for object instances. That should be qualified; there are languages that do treat classes as instances of a "Class" or "Metaclass" type. These languages do support polymorphism for both instance and class (static) methods.

C#, like Java and C++ before it, is not such a language; the static keyword is used explicitly to denote that the method is statically-bound rather than dynamic/virtual.