Stubbornness is often observed when opposing authority of some kind. We especially see this in children when they resist parents, teachers, and siblings. What is the principal cause of this?

What you are truly observing in cases like your example of defying authority is bringing to bear oftentimes emotion of some kind. So one is not simply checking something against their knowledge base and belief set and replying according to how that catalogue of information informs them about what to do or not do. Many times people are reacting to emotion as they go about their lives, and that colors things and it will influence judgment as well, so there may be a difference between the decisions people make from a state of calm reflection and a state of mind where they are experiencing heightened emotions, feeling pressured, and reacting to the stress. Under such circumstances, stubbornness to resist an influence that part of the self is seeing as a danger can be prudent, but there are certainly many more instances when people who have suffered so from chronic anxiety, and this includes a high percentage, may be too reluctant to embark on something new and will refuse an invitation, or ignore guidance, or fight against attempts to control or influence them, as is the case with opposing someone in authority. Keep in mind that the young, in particular, have little life experience to guide them. They will be highly influenced by what has happened most recently, so if there has been a circumstance where a parent, for example, has punished them or been critical and now wants them to cooperate in some way and makes a perfectly reasonable request for that cooperation, the young person might still be smarting from being hurt in a previous parental encounter, and that emotion will alter their perception of the request and cause them to dig in their heels and say "no." Being oppositional is a kind of primitive way of reacting to an attack. It is instinctive and must be overridden by learning and growth for the person to not automatically refuse a request as an automatic assumption that it will be an imposition, that it is probably unfair, and why should they give up anything simply because someone wants them to do it? This is a selfish perspective which is typical of young children who must learn to express a greater moral perspective. This is learned over time in wisdom gained from life experience as they interact with people around them, and can begin to model the behavior as they see that it will help them to fit in and receive less criticism and fewer penalties from those in authority if they can come to an understanding that the expectations placed on them may in fact have some higher purpose, and this will help them to make accommodations to the realities of existence, that they are not the center of things and must find ways to fit in and be cooperative to help things go well. The danger in young people, in particular, is for the resistance to authority becoming an ingrained habit. This is most likely when there has been a major grievance from neglect or ill‑treatment causing them to form a grudge against the perpetrator, even a parent who naturally will assume and act on the belief they deserve respect and expect that of their offspring. Oftentimes there are distortions on both sides where a parent might be less sensitive than desirable in understanding the feelings of their children, and treat them in an arbitrary and demanding way that might reinforce the inner sense of being threatened, in being dominated by the adult parent. This is why there needs to be a good balance in the tone and conduct of parents always, to be respectful to their children. In a sense, they deserve the same respect as an adult because their inability to understand and fully appreciate the parent’s perspective, lacking as they do in adult experience and wisdom, does not mean they need harsh treatment to always force them to obey. We would say they actually need greater leeway and latitude and understanding on the part of the parents, to put themselves in their children’s shoes and understand they will have a harder time cooperating because they may feel things much more keenly than one would expect, and what seems simple and straightforward to the adult might be highly stressful and a dire turn of events to the child. Even having to stop play to attend to a necessary duty or circumstance is highly distressing and is seen daily with infants and young children at bedtime when it seems like the greatest of tragedies being asked to, in effect, stop living if only for the sleep time. So we like this question because it gives an opportunity to talk about the differing perspectives in many life situations and to teach that there are always opportunities to learn from pausing to consider the perspective of the other party when there is a disagreement about stubbornness being perceived. This would go a long way to helping people find ways to reach a compromise and to negotiate more effectively with one another about their desires and avoid making snap judgments to characterize and label other people. If done harshly, it not only attacks and wounds them, it may well represent a new obstacle to making any progress towards changing things in the way desired by the attacker and will be counterproductive.