Why can't I assign a parent class to a variable of subclass type?

There is no reason which has something to do with the memory. It's much more simple. A subclass can extend the behaviour of its superclass by adding new methods. While it is not given, that a superclass has all the methods of its subclasses. Take the following example:

public class Parent {
    public void parentMethod() {}
}

public class Child extends Parent {
    public void childMethod() {}
}

Now let's think about what would happen if you could assign an instance of Parent to a variable of type Child.

Child c = new Parent(); //compiler error

Since c is of type Child, it is allowed to invoke the method childMethod(). But since it's really a Parent instance, which does not have this method, this would cause either compiler or runtime problems (depending on when the check is done).

The other way round is no problem, since you can't remove methods by extending a class.

Parent p = new Child(); //allowed

Child is a subclass of Parent and thus inherits the parentMethod(). So you can invoke this method savely.

The answer is too late.

I believe we can explain it in terms of memory. Maybe I'm wrong but this is what I'm thinking about this scenario.

// Assume, Required 2KB for execution
public class Parent {
    public void display(){      
        System.out.println("From Parent");
    }
}

// Total memory required for execution : 4bk
public class Child extends Parent {
    @Override
    public void display() {     
        super.display(); // 2KB
    }
    
    public void sayHello() {     
        System.out.println("From Child - Hello"); // 2KB
    }
}



   //2KB expect    //4KB assigned
     Parent parent = new Child();
        
   //4KB expect    //Only 2KB is assigning
     Child child = new Parent();

Here the 'CHILD' class variable is expecting 4KB memory, but we are trying to assign 2KB 'Parent' class objects to it. So the compiler throwing exception.