MikeH

Answer: It wasn't Teasle that shot, it was one of the other police. Teasle even shouts at them to stop shooting.

Answer: Possibly to lull him into a false sense of security and then shoot him when his guard was down.

raywest ★

Chosen answer: He is never shown on camera to definitely kill more than one person (the shooter in the helicopter); the police cars flip over and crash, but the people inside are not shown to be dead, so it is possible they survived.

Twotall

Answer: Teasle is a "my way or the highway" type of guy, as evidenced by his actions and the people he has on his team (they are either very aggressive, or extremely passive and do whatever they are told). When Rambo escapes, he is hell bent on ensuring that justice is served (even though he fabricated the crimes basically), so much so that he gets abusive and obsessed with serving it. he knows the national guard guys are likely to shoot first and ask questions later, so he tells them that he wants him alive, so that he can ensure justice if served. He is basically akin to Batman - justice will be served at any costs, except for killing them in cold blood.

oldbaldyone

Answer: Teasle wasn't "desperate to kill Rambo." Throughout the movie his goal isn't to kill Rambo, but rather to stop him. Teasle is a man of the law and wants to capture Rambo and bring him to justice.