Intransigence is the noun: a stubborn unwillingness to change your ideas or behaviour, in a way that other people find unreasonable. It is not just being sure of yourself. It is refusing to meet anyone halfway, even when a little movement would help. News writers use it about talks, politics, and long arguments — “both sides accused the other of intransigence.” It is a formal word. You would not usually use it of a child who will not eat vegetables, unless you were being wry and heavy. Though actually, the person showing intransigence often feels they are being principled, not difficult; the word itself already takes a side and says the stubbornness has gone too far.