Static factory disadvantage over constructor

I am going through Effective Java. The very first item makes a convincing case for static factory methods over constructors.

I didn't get the first disadvantage which is

The main disadvantage of providing only static factory methods is that classes without public or protected constructors cannot be subclassed.

Why do i need to subclass the class having static factory method since static methods can't be inherited?

Can someone please explain.

Suppose you have a class called Person:

class Person {
  public static Person createWithFirstName(String firstName) {
    return new Person(firstName, null, null);
  }
  // etc. - more factory methods

  // private constructor
  private Person(String firstName, String lastName, String nickname) { }

  // useful method
  public String getDisplayName() { }
}

It's all good and dandy. But now you also need a class called Programmer, and you suddenly realize the programmers are persons too!

But all of a sudden, you can't just

class Programmer extends Person { }

since Person doesn't have any public constructors.