Nothing To Be Frightened Of There

I think Harry has worked hard to convince himself of these things.  He is working hard to believe that Hogwarts is safe now--after all, his first-born has apparently been attending without major incident for three years.  And I think he wants to encourage Albus and himself by saying that Hogwarts will be the making of him.  Harry arrived at Hogwarts already in the limelight because he was famous for something he couldn't remember*.  He might have sensed that Albus, who looks so much like his father--a phenomenon with which Harry is familiar--is afraid of the expectations that come with being Harry Potter's son.  And again, it seems to have worked out for James, who has cultivated a prankster/Marauder-grandson/Weasley-twin-nephew persona, which is a significant departure from Harry's trouble-finds-me attitude.

As kindly as Harry means it, this statement turns out to be kind of grim foreshadowing, as Albus ends up struggling a great deal both with magic and relationships, then abruptly trying to prove himself and nearly heralding in a new era of Voldemort, in which he does not even exist.

*except when in the presence of dementors or, vaguely, when having a nightmare

--AK