It is significant in the context of his greater story because it shows he is his own person even with a piece of Voldemort living in him.
This is repeatedly a theme of Harry’s character. That he isn’t Voldemort because he makes different choices.
Rowling wanted it to be conveyed though in Harry’s character clearly that he could easily have been someone like Voldemort.
Harry could have easily chosen a path like that after discovering he had powers of Voldemort’s. He could have decided he wanted to be a dark wizard too.
The danger that Harry might eventually give in and go over to the dark side as it were is repeated at certain points throughout the Harry Potter book series, but mostly in the earlier installments
A. because he found out from Ron that Slytherin had a reputation of producing dark wizards, and Harry hated the idea.
Later in Chamber of Secrets and Deathly Hallows only a true Gryffindor can produce the sword that could save his life when up against "He Who Must Not Be Named" aka "You Know Who" aka Voldemort.
Explanation:
Because only a true Gryffindor can produce the sword of Gryffindor
