I know it's a very important safety command, a little different from "Leave it". I taught all my other dogs this with a very low stern, no-nonsence voice. If they still didn't drop it, I grab the back of the neck with one hand and hold the head down. (keeps them from swallowing it) Then say "drop it" in the low mean voice again. They then drop it.
This doesn't work with Tony. My low scary voice doesn't scare him at all. When he has something bad in his mouth, usually sticks, twigs, dirt, he does come to me with it, and he will trade it for a treat, but I don't always have a treat handy. I have to put hand in his mouth, and do a sweep all around to get it out. He lets me do that, but will not drop it. Yesterday I saw him running the yard with this black limp thing hanging from his mouth. His first mole. He came to me with it but would not drop it. I was afraid he would swallow it but really did not want to reach in his mouth to pull it out. Eww. I finally pulled his jaw open with head down and it dropped out.
Any advice on teaching "drop it"?
When I was with Bo, he didn't know either "leave it" or "drop it" and with him the drop it was the hardest one, but he finally got it. What I found worked with him, as he was like Tony in that he expected a treat for dropping, I faked him out! I would start to put my hand in my pocket as I said "drop it" in a firm, but not mean voice. He dropped it immediately expecting his treat, I grabbed what he dropped so he couldn't take it again, did not give him a treat, but instead a big "GOOD BOYYY!!!!" and rubbed his head, made a big deal. He fell for it every time, though I wasn't with him long enough to confirm the fake out works long term!
We taught Kai drop it by first playing with her with a toy. We would say "drop it" and get the toy out of her mouth(got it out by gently squeezing either side of her jaw to open her mouth), give her a treat. Continued until she dropped it on her own, then treat. Now we don't even give her a treat all the time and she does it for everything, not just toys.
Here's a problem I found with the trade method: Dog has something in mouth that he REALLY doesn't want to drop; he knows you will take it away once he drops it. You offer a high value treat in exchange. He stops to weigh possibilities. (Never forget how smart Labs are.)
1. Keep dead chipmunk and miss out on treat
2. Drop dead chipmunk and get treat but lose chipmunk
3. Swallow dead chipmunk and get treat.
Option 3, have cake and eat it too, sounds very good to Lab.