How to correctly cast a class to an abstract class when using type generics?

This is a very frequently asked question. Let's rename your types:

abstract class Fruit { }                    // was BaseViewPresenter
abstract class FruitBowl<T> where T : Fruit // was BaseView
class Apple : Fruit { }                     // was LoginPresenter
class BowlOfApples : FruitBowl<Apple> {  }  // was LoginView

Your question now is:

I have a BowlOfApples, which inherits from FruitBowl<Apple>. Why can I not use it as a FruitBowl<Fruit>? An apple is a fruit, so a bowl of apples is a bowl of fruit.

No, it isn't. You can put a banana in a bowl of fruit, but you can't put a banana in a bowl of apples, and therefore a bowl of apples is not a bowl of fruit. (And by similar argument, a bowl of fruit is not a bowl of apples either.) Since the operations you can legally perform on the two types are different, they cannot be compatible.

Here is a photo of StackOverflow legend Jon Skeet demonstrating this fact:

The feature you want is called generic contravariance, and it is supported only on interfaces and delegate types when the compiler can prove that the variance is safe, and when the varying type is a reference type. For example, you can use an IEnumerable<Apple> in a context where IEnumerable<Fruit> is needed because the compiler can verify that there is no way that you can put a Banana into a sequence of fruit.

Do a search on "C# covariance and contravariance" on this site or on the web and you'll find many more details about how this feature works. In particular, my series of articles on how we designed and implemented this feature in C# 4 starts here: http://blogs.msdn.com/b/ericlippert/archive/2007/10/16/covariance-and-contravariance-in-c-part-one.aspx

I accepted Eric's answer since it provides a great explanation of why what I wanted wasn't possible, but I also thought I'd share my solution in case anyone else runs into this same problem.

I removed the generic type parameter from my original BaseView class, and created a 2nd version of the BaseView class that included the generic type parameter and specifics for it.

The first version is used by my .Resolve() method or other code that doesn't care about the specific types, and the second version is used by any code that does care, such as the implentation of a BaseView

Here's an example of how my code ended up looking

// base classes
public abstract class BaseViewPresenter { }
public abstract class BaseView : UserControl 
{
    public BaseViewPresenter Presenter { get; set; }
}

public abstract class BaseView<T> : BaseView
    where T : BaseViewPresenter
{
    public new T Presenter
    {
        get { return base.Presenter as T; }
        set { base.Presenter = value; }
    }
}

// specific classes
public class LoginPresenter : BaseViewPresenter { }
public partial class LoginView : BaseView<LoginPresenter> 
{
     // Can now call things like Presenter.LoginPresenterMethod()
}

// updated .Resolve method used for obtaining UI object
public BaseView Resolve(BaseViewPresenter presenter)
{
    var type = model.GetType();
    var viewType = _dataTemplates[type];

    BaseView view = Activator.CreateInstance(viewType) as BaseView;
    view.Presenter = presenter;

    return view;
}