In order to understand why Harry Potter is the protagonist in Order of the Phoenix, one must understand what "protagonist" means. A protagonist is the main figure in a story. Overall, even though there are many moving parts in the story, Harry is still the primary figure and every event follows him throughout the wizarding world.
The way one can tell who the central character in a work is is to look at the point-of-view of a story. Throughout the entire series, the narrator is third-person limited except for one chapter in Harry Potter and Half-Blood Prince, when the first chapter follows Snape. But throughout the series, Harry is the protagonist. The reader follows Harry's every action and is able to understand a bit about Harry's motivation.
While Order of the Phoenix has many moving parts, each and every scene is about Harry.