On Criminal Minds as BAU agent (FBI)

So there was one scene where this girl who wasn't much more than a teenager has a small surgical scalpel in her hand. DH is wearing an FBI vest I believe, tall, lean and muscular. She's a few feet in front of him and he's got his gun out and warns her to drop the blade. She chooses to rush at him, and he immediately shoots her point blank dead. He looks like he could have chosen other means to subdue her, or avoid the attack and try something else, but he simply just shot her. This didn't look right to me, especially on a TV show. I would like to think a trained, strong FBI field agent wouldn't be afraid to grapple with a young lady with a 1-1/2 inch scalpel in her hand.