Why do we need a private constructor?

Factory

Private constructors can be useful when using a factory pattern (in other words, a static function that’s used to obtain an instance of the class rather than explicit instantiation).

public class MyClass
{ 
    private static Dictionary<object, MyClass> cache = 
        new Dictionary<object, MyClass>();

    private MyClass() { }

    public static MyClass GetInstance(object data)
    {
        MyClass output;

        if(!cache.TryGetValue(data, out output)) 
            cache.Add(data, output = new MyClass());

        return output;           
    }
}

Pseudo-Sealed with Nested Children

Any nested classes that inherit from the outer class can access the private constructor.

For instance, you can use this to create an abstract class that you can inherit from, but no one else (an internal constructor would also work here to restrict inheritance to a single assembly, but the private constructor forces all implementations to be nested classes.)

public abstract class BaseClass
{
    private BaseClass() { }

    public class SubClass1 : BaseClass
    {
        public SubClass1() : base() { }
    }

    public class SubClass2 : BaseClass
    {
        public SubClass2() : base() { }
    }
}

Base Constructor

They can also be used to create “base” constructors that are called from different, more accessible constructors.

public class MyClass
{
    private MyClass(object data1, string data2) { }

    public MyClass(object data1) : this(data1, null) { }

    public MyClass(string data2) : this(null, data2) { }

    public MyClass() : this(null, null) { }
}