As I was saying, there are many ways to exasperate and provoke your children to wrath. When our kids react in sin we usually only judge their reaction, failing, like most basketball referees, to observe the foul play that provoked the reaction. This is especially harmful to the home's holiness when the instigator was, in fact, you. Which is why Paul in Ephesians 6:4 warns us fathers. Because, you know, worse case scenario we could be setting a millstone around their necks.
"Fathers, do not provoke your children to anger, but bring them up in the discipline and instruction of the Lord." This is the famous "nurture and admonition" (KJV) verse. Interesting that we struggle to decide in translating paideia whether it should be discipline or nurture, since neither our words "education" or "rear" transmit the idea of the process of raising a human, of forming a man. The discipline and instruction of the Lord, y'all, is a whole-of-life labor until the children are no longer yours. Fathers are responsible for the holistic formation of their little humans.
So, according to Paul, instead of provoking your children, you ought to discipline and instruct them. Which suggests that if you discipline and instruct them, you will not be provoking them. Hm...yeah, seems like that holds water.
Your children will sin, with or without your help. But it is important for their growth and sanctification that you shepherd them. There is only good in considering your child's frame.
One way to consider your child's frame is remember that you are fallible, and to set up a family structure that reflects that. Remember that your family belongs to God; Christ is the King.
Your children should see your wife discussing things openly with you. She should be able to suggest, challenge, and even disagree with you (depending on the weight of what is being discussed) in front of the children. Your authority can handle it, because your wife is a godly woman.
Your children should also believe that they can have opinions and disagree with dad. This is something that will have more and more amplitude as the children grow, but begins at a young age. And it should be taught. In our family, the kids must always say "Yes, sir" and begin the task before they express their objections. And their objection might very well be "Mom said not to throw that away because she'll need it tomorrow." And my response might very well be, "Oh, never mind then." What they may not do is express the objection before they begin to obey.
If your fifteen-year-old realizes that you're being a stubborn fathead about a particular thing and has had no nurturing/disciplining/education in how to handle his disagreement with you, he will have no categories for pushing back at you in a respectful and honoring way. He will see only two choices: to sin by submitting against his conscience, or to sin by rebelling against you. It is your responsibility to shape the family culture in such a way that he can disagree with you. Many difficult situations will be eased by the simple happening of a conversation; often the assumption of responsibility by you will ease his conscience and he can go ahead with whatever it was knowing that now it's on dad (remember, in this situation you're being a stubborn fathead, and are wrong).
It is also vitally important that your children be able to tell you when something is harming them, whether it is something they are doing, or you are doing, or a third party. If your children are afraid of provoking your wrath by telling you something bad about your favorite sports team, or another child, or a teacher, or a philosophy, or a habit of theirs, or a behavior of yours, you could be causing your little one to stumble. They must know that even if they are completely in the wrong, whether irrational, or fearful, or petty, or wicked in their telling you, that you will hear them, and forgive them, and nurture and instruct them.
Thus endeth this post, except for the video below, which includes an anecdotal illustration of why kids should speak and parents should listen.