Why did the werewolf kill an "innocent" victim?

No, I'm trying to say the Reverend wants to believe he could never do those things. He is unable to cope with the werewolf side of him, cannot accept that he can and does hurt innocent children. Even Marty was not aware of a werewolf until he saw it, so I don't think it attacked him because he was on to him, not the first time. Also, listen to his tone. He has Marty trapped in the old bridge. He's coaxing, trying to earn his trust. It's "I would never willingly harm a child...now take my hand..." That's not the "good guy" in the bridge with Marty. That's the "wolf", the other side, trying to lure him in. But yes, historically, it is believed that serial killers are werewolves, in a sense that they were born from a superstitious time where these crimes were often imagined as being committed by "beasts". The Werewolf Book is chock full of examples. Starrett is a complicated guy. It's really difficult to sum him up easily. There's a book about him called A Stranger in the Family, but you could probably just as easily read about him online for free.

Directly to the question, I don't believe an answer is ever spelled out to Brady's death, but we know the Reverend Lowe is fond of her (again, by his tone, "Hello, Jane!") And that Brady can be a "cruel and unsympathetic" boy, a prankster who takes things too far. He may have roused Lowe's anger with the cruelty he showed Janie.

I think Brady was victim to the purely wolf side. The priest says he would never willingly hurt a child. So in a sense, the monster was out of control beyond the Reverend. It's simply a case of predator killing prey. Also, Marty knows nothing of his true identity when he is first attacked on the bridge while playing with the fireworks, it isn't until the Rev shows up with the same wound as the wolf that Marty and his sister put it together.