Stick up your ass
When someone simply will not budge or admit wrongdoing, despite knowing very well that they're wrong and that fact being plain obvious. When someone is being extremely stubborn for no reason, especially for something relatively minor, they have a stick up their ass.
Dave: Son I want you to go pick three dandelions and bring them back to me, I can't because my back hurts.

Son: No dad, I don't want to.

Dave: oh come on you can't just do it, it's three flowers son.

Son: No, I don't feel like it, do it yourself

Dave: Son, why do you have a stick up your ass? It's such an easy and simple task that you'd already be done with if you didn't argue with me.