Use the noun orneriness to talk about the quality of being stubborn. You might refuse to babysit a mean and obstinate child again after experiencing his orneriness.
When a person is ornery, he refuses to listen to reason and seems willfully determined to do the opposite of what you'd like him to do. You can talk about his orneriness when you're describing him to someone else. The root of orneriness, the adjective ornery, started as a regional pronunciation of the word ordinary, and its 1816 meaning was "commonplace, or of poor quality." Toward the end of the nineteenth century, the word came to mean "cantankerous or mean."