Why cannot a non-member function be used for overloading the assignment operator?

The assignment operator can be overloaded using a member function but not a non-member friend function:

class Test
{
    int a;
public:
    Test(int x)
        :a(x)
    {}
    friend Test& operator=(Test &obj1, Test &obj2);
};

Test& operator=(Test &obj1, Test &obj2)//Not implemented fully. just for test.
{
    return obj1;
}

It causes this error:

error C2801: 'operator =' must be a non-static member

Why cannot a friend function be used for overloading the assignment operator? The compiler is allowing to overload other operators such as += and -= using friend. What's the inherent problem/limitation in supporting operator=?