Sure, Order of the Phoenix isn't the first time we meet Cornelius Fudge, but it's probably the Minister of Magic at his worst. Even though Harry and Dumbledore have both explained to him that Voldemort is alive and well and bent on taking over the wizarding world, Fudge will not hear of it.
The Minister is so overcome by fear that he's totally dropping the ball:
SIRIUS BLACK: Fudge is using all his power, including his influence at The Daily Prophet, to smear anyone who claims the Dark Lord has returned.
HARRY POTTER: Why?
REMUS LUPIN: The Minister thinks Dumbledore's after his job.
HARRY POTTER: But that's insane! No one in their right mind could believe that Dumbledore—
REMUS LUPIN: Exactly the point. Fudge isn't in his right mind. It's been twisted and warped by fear. Now fear makes people do terrible things, Harry. The last time Voldemort gained power he almost destroyed everything we hold most dear. Now he's returned, and I'm afraid the Minister will do almost anything to avoid facing that terrifying truth.
In a way, we kind of feel bad for Fudge. He's in a tough spot. He really doesn't want to be the one to tell people the most terrible dark wizard of all time has returned. No politician wants that to happen on his watch. But the solution isn't to lie to people. It's to take responsibility and to move forward so that people can be safe. You know, grown up stuff.
But Fudge seems more worried about losing his job than securing the wizarding world. He's convinced himself that there's no problem so he can keep pretending like all is well. That's a recipe for disaster.