Stephen Goff's article on Arnsberg brings up some clues from his past as to why he was relieved.
Although Arnsberg was a vital part of the 2003 World Series championship team in Florida, Examiner.com learned that he got relieved of his duties following the team's successful year due to the organization not agreeing with the way he was developing the young arms.
This agrees with an interview Astros County conducted with Joanna from Hum and Chuck, a Blue Jays blog, in November 2009 - after Arnsberg had been hired by the Astros:
I probably don't pay enough attention to other teams, but there seemed to be an excessive amount of guys going under the knife and being generally injured. And not old, broken down guys. But I'm talking about kids. Off the top of my head, Shawn Marcum, BJ Ryan and Jesse Litsch had TJ under Arnsberg's watch. Dustin McGowan, who is insanely talented, has been injury plagued. He is diabetic, which contributes to his frailty. Ryan was released from the Jays after coming back from TJ as a shadow of his former self.
All of this might just be coincidence or just the guys, but it might also be conditioning. I can't find the data to back it up, but it seems a lot of guys were injured under his watch on the Marlins. I know for sure AJ had his Tommy John surgery in that time. So again, young guy breaking down.
Clues? We'll find out.