oop - Polymorphism in java: Why do we set parent reference to child object?

Question

I want to understand the use-case of setting a parent reference to a child object. Example: Dog class extends Animal class. (No interfaces, mind it) I would normally create an object of Dog like this:

Dog obj = new Dog();

Now, since Dog is a subclass of Animal it already has access to all of Animal's methods and variables. Then, what difference does this make:

Animal obj = new Dog(); 

Please provide a proper use-case with an code snippet of its use. No theoretical articles about 'Polymorphism' or 'Coding to interfaces' please!

Code:

public class Polymorphism {
    public static void main(String[] args){
        Animal obj1 = new Dog();
        Dog obj2 = new Dog();
        obj1.shout(); //output is bark..
        obj2.shout(); //output is bark..        
    }   
}

class Animal{
    public void shout(){
        System.out.println("Parent animal's shout");
    }       
}

class Dog extends Animal{
    public void shout(){
        System.out.println("bark..");
    }
}

class Lion extends Animal{
    public void shout(){
        System.out.println("roar..");
    }
}

class Horse extends Animal{
    public void shout(){
        System.out.println("neigh");
    }
}

Output is the same for both the cases. Then why do we set parent reference to child object?

Answer 1

Let me code some time.

List<String> list = new ArrayList<String>;
list.doThis();
list.doThat();

Oh wait ..I'm gone mad. I want to use LinkedList instead of ArrayList

List<String> list = new LinkedList<String>;
list.doThis();
list.doThat();

Yup, I have to change only declaration part. No need to touch all of my code. Thanks to programming to interfaces and with super classes.