Why is .Equals() dispatched dynamically and == dispatched statically?

Question

I asked this question recently: When would == be overridden in a different way to .equals?. I was referred to this article: https://ericlippert.com/2013/10/07/math-from-scratch-part-six-comparisons/

I don't fully understand the reference to static method calls (== and !=) and dynamic method calls (.Equals()). Please see the code below:

public class A
{
    private string Field1;
    private string Field2;

    public A(string field1, string field2)
    {
        Field1 = field1;
        Field2 = field2;
    }

    public static bool operator ==(A a1, A a2)
    {
        throw new NotImplementedException();
    }

    public static bool operator !=(A a1, A a2b)
    {
        throw new NotImplementedException();
    }

    public override int GetHashCode()
    {
        throw new NotImplementedException();
    }

    public override bool Equals(object obj)
    {
        throw new NotImplementedException();
    }
}

public class B : A
{
    private string Field3;
    private string Field4;

    public B(string field1, string field2, string field3, string field4)
        : base(field1, field2)
    {
        Field3 = field3;
        Field4 = field4;
    }

    public static bool operator ==(B a1, B a2)
    {
        throw new NotImplementedException();
    }

    public static bool operator !=(B a1, B a2b)
    {
        throw new NotImplementedException();
    }

    public override int GetHashCode()
    {
        throw new NotImplementedException();
    }

    public override bool Equals(object obj)
    {
        throw new NotImplementedException();
    }
}

and the test below:

A a1 = new B("hello","hello","hello","hello");
A a2 = new B("hello", "hello", "hello", "hello");
var test1 = a1.Equals(a2);
var test2 = a1 == a2;

I do not understand the reason it is implemented this way? I have spent the last hour this evening Googling this, however I am still not clear and hence the reason for the question. Why is .Equals() dispatched dynamically and == dispatched statically?

Answer 1

.Equals() is a virtual instance method, which is subject to normal overriding rules / polymorphism.

== is syntactic sugar for the static .op_Equality() method, which is a normal static method call with two parameters and therefore does no dynamic dispatch at all.