Most dogs does not like to have their heads gripped from above, hold on to and forced to have their mouth inspected by a stranger. That is quite natural. But most dogs should not have to have a problem with having their owner doing this or doing this with their owner backing them up.
This has to do a lot with trust and experience. Think of yourself. If you are comfortable to lay your head in some ones lap in front of the TV. If you are comfortable to kiss somebody. Than you will let them help you with an aching tooth too? But if you are not comfortable with some one you are close with to let them softly strike your face, even when you are relaxed, then letting them open your mouth and inspecting your teeth in a stress full environment is far from a positive experience.
With a puppy you can start with cuddling, massage, striking the face and the corner of the mouth. Let them take food from your mouth- This is all about earning trust. Showing that you are relaxed, yawning, and kind and do not want to make any harm. Make the dog comfortable with sitting in your lap (even a Grate Dane can fit the first weeks). Use this time to make them comfortable with you touching, striking, massaging. So that if it is hurt, if an accident appear, they are comfortable with the touching even if the pain is new and scary.
If you make your puppy experienced with slow, soft movements as young, the faster moment of showing its teeth in the ring will be less complicated.
If you have an 4 month old and has totally forgot to do this, and find that your puppy finds your hands more than fun to play with when you try to practice the teeth showing or if you have an older dog that does not really appreciate to show its teeth or having the mouth inspected. This might be worth trying.
First of all, make sure that your dog is exercised and not in pain. (A lot of dogs has tooth problems and tartar that makes their mouth ache. Make sure that is not the reason for the unwillingness to show their teeth, if possible.)
Well all of us write here, both humans and dogs ;) At least that was the plan but it seems it´s mostly me Robyn who´s attached to the keyboard...