Jared Leto's character doesn't even get a name. He's just so beautiful that he's called Angel Face. He joins fight club, and then Project Mayhem, and then starts being doted on by Tyler. This makes our main character jealous, even though our main character is Tyler, so he's jealous of himself for giving attention to a hot guy. Or something.
Sweaty homoeroticism aside, what our narrator is really jealous of is that fact that Angel Face knows the ultimate plan of Project Mayhem and our narrator doesn't. He's being kept in the dark by the Tyler side of his personality, and, since Tyler has brought out our narrator's latent aggression, the only way he knows how to handle it is to beat the snot, blood, and teeth out of poor Angel Face, turning his face into meat loaf (but not Meat Loaf) in the process. "I felt like destroying something beautiful," our narrator says to explain his brutality.
Angel Face never speaks. In the world of Fight Club, beauty doesn't have a voice. Only the ugly side of human nature is allowed to speak.