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

This is an implementation of a principle which says -

Program to an interface, not to an implementation.

As an example, if you design a method to accept a reference of type Animal, then in future you can easily pass an= Cat implementation to it (provided of course that the Cat is a sub-type of Animal.

Which means -

public void doSomethingWithAnimal(Animal animal) {
    // perform some action with/on animal
}

is much more flexible than -

public void doSomethingWithAnimal(Dog d) {
    // your code
}

because for the first method, you can easily do something like -

doSomethingWithAnimal(new Cat());

if you ever decide to create new Cat type, inheriting from Animal.

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.