Well, perhaps Harry is fed up with the false or malicious stories in the Daily Prophet in the fanfic and decides to take action to destroy it. Maybe he uses magic to burn all the copies or disrupt the printing process.
In this fanfic, Harry might destroy the Daily Prophet for various reasons. One could be that the newspaper has been spreading lies about him and his allies for a long time. So, he decides to put an end to it. He could use powerful spells like Reducto to blast their headquarters or Confundo to make the staff confused and unable to continue their work. This would be a significant event as the Daily Prophet has a great influence in the wizarding world, and Harry's act of destruction would send a strong message that he won't tolerate their false reporting any longer.
In the 'harry destroys daily prophet fanfic', it could be that Harry has finally had enough of the Daily Prophet's slander and misinformation. He might go on a rampage through their offices, using spells to break their printing presses and scatter their quills. This could be his way of standing up against the media that has been causing so much trouble in his world. It could also be a symbolic act of him breaking free from the false narratives they've been spreading about him and his friends.