Why does Console.Out.WriteLine exist?
Console.WriteLine is a static method. Console.Out is a static object that can get passed as a parameter to any method that takes a TextWriter, and that method could call the non-static member method WriteLine.
An example where this would be useful is some sort of customizable logging routines, where you might want to send the output to stdout (Console.Out), stderr (Console.Error) or nowhere (System.IO.TextWriter.Null), or anything else based on some runtime condition.
Brad Abrams (The founding member of both CLR and .NET framework at Microsoft) says the following.
Console.WriteLine() is simply a shortcut for Console.Out.WriteLine. Console was overloaded by WriteLine propery to make that much easier to write.
Source: Book "The C# Programming Language by Anders Hejlsberg".