This has been probably discussed but I'll break the ice.
Why was Lutz such a-hole? He was verbally abusive, making threats and paranoid. The good guys went out of their way to solve the alphabet crimes but Lutz was always in their way to stop them as if he's trying to cover something. Maybe he was following protocols but if it wasn't for the good guys, the baddies would've succeeded.
I don't know why he was so mean to them. Maybe he expected more from them so he yells at them or something.
shareLutz is a power-hungry politically motivated asshat, and only made Chief because he commands like a dictator. His incompetence leans from the inability to use his mind to solve cases and dig a little deeper into these tricky ones. He only sees what he wants to see, nothing more, nothing less. That's not a detective. That's a closed mind. Because of this weakness and his lack of intelligence, he replaces it with anger issues, a sign of insecurities, and acts like a bully, thinking that will receive him a lot of respect from his officers. Unfortunately, it is also results in him showing that no one else can possibly do their jobs either because he won't work with them one officer to another.