One of the reasons the jaw can be tense is because we have set it against the people who have wronged us. Or we are clenching our teeth, trying not to say the thing we feel bitterly to be true, but we know shouldn't be said out loud.
When we go to loosen the jaw, for the first or the hundredth time, we run into the feelings that helped create the tension. They can be bigger than you might think. The jaw can be more resistant to loosening than seems rational.
Letting go of jaw tension often means letting go our ideas about who other people should be, what they should say, how they should act. It's true, we use our jaw muscles all day long, talking and eating, talking and eating. They will probably be tense even on the day we are enlightened masters. The more spiritual work we can do, though, the lighter the burden on our jaws will become.
The more we can trust that our singing is a good gift, to ourselves and the people around us, the easier it will be to open our mouths and let the sound out.
Singing well usually requires forgiving other people. It always requires we soften our relationship with ourselves.