Stubbornness can be a good quality in a person if it is tempered with wisdom. When it leads to obstinacy and contradiction, the stubborn one needs to be able to weigh the pros and cons and know when to quit. Funny how being obstinate or contrary subsides when we no longer dig our heels in. "Stubbornness is as iniquity and idolatry" (1 Samuel 15:23) when it means rejecting the word of God for Satan's way.
There are a number of encouragements in the Bible to "stand fast." God is pleased with one who holds fast to what is right. The word stubborn seems to mean holding fast no matter how wrong we are. God wants us to hold fast when we are right. Paul encouraged the Philippians to hold fast to that which is good and to stand fast in the Lord (1 Thessalonians 5:21 and 2 Thessalonians 2:15). Be stubborn for the right things.