I am developing an internal class that implements an internal interface. Can anyone explain why I cannot declare my method as internal, why I am getting the following error
Simply put: because that's the way the language designers designed it. Even in internal interfaces, the methods are implicitly public. It does make things simple, but it's a pain in other ways.
If you want a public class where you want to "hide" the use of an internal interface, you could use explicit interface implementation - although that has other drawbacks.
Of course, if your class is internal then it doesn't matter that the methods are public anyway - other assemblies aren't going to be able to call the methods because they can't see the type.
I definitely agree that C# (or .NET in general) hasn't been designed as carefully as it might be around internal interfaces.
In terms of exactly why you're getting an error message - section 13.4.4 of the C# 4 spec (interface mapping) is the reason. Implementations are only found for nonstatic public members and explicit interface member implementations - and if there are any unimplemented members in the interface, an error occurs.