His shaking hand is his gun hand. If you shake that hand, you are tying up that hand. If you’re a “bad” guy, you could suddenly over take him. He (sadly) has to think like that. All the time he has to imagine what you, yes even you, the soccer mom or the man in the suit on his way to work, might do to him in the worst case scenario.
His shaking hand is also his dominant hand, so offering it to you could leave him vulnerable. I want him to return home to me, so I don’t want him leaving himself open to you by shaking hands.
If you’re inside a car while shaking hands, you could grab a hold of his hand, floor the vehicle, and drag him along.