Stubbornness is not a virtue.
It is always a vice.
It refers to a deep attachment to error.
We can discern truth through study, prayer, and listening to others.
Problem is that many people, especially in the west are so used to the individualistic society we live in, they trust only their judgment, or the judgment of their families, and will not listen to other people, the common understanding of other trads etc. etc. There is little docility of soul.
I remember a few months ago being reminded of this with a certain person who was so convinced of her own opinion on something. I patiently tried to explain that no other trad, or any reasonable person, would see things the way she was seeing them. Instead of stopping and pondering this truth, she doubled down, and said, "well they're all wrong". This is the very definition of prideful stubbornness. And to make things worse had the audacity to accuse me of being the one who was stubborn.
It's important to remember that pride is the WORST of all sins. Because by pride a man pulls out his own eyes. The eyes of his soul that is. Many other sins, are sins of weakness of the flesh. Which, when repented from, get compassion from God. But pride is so diabolical, because it puts one on an equal footing with God. It governs all the other sins in a way, just as humility does for virtue.
Now what simpleman may be referring to is attachment to the TRUTH. This is a very different thing. It can appear prideful to stubborn or just pure stupid people, but it is a very rational acceptance of the superiority of the supernatural over the natural, or the simple acceptance of the natural law, against someone who won't accept it.