As a parent you have authority because God calls you to be an authority in your child's life. You have the authority to act on behalf of God. As a father or mother, you do not exercise rule over your jurisdiction, but over God's. You act at his command. You discharge a duty that he has given. You may not try to shape the lives of your children as pleases you, but as pleases him.
Lets read how God directed Abraham.
For I know him, that he will command his children and his household after him, and they shall keep the way of the Lord, to do justice and judgment; that the Lord may bring upon Abraham that which he hath spoken of him.
As you see here Abraham is on God's errand. He is performing a task on God's agenda. God has called him to these things. He is not freelancing. Abraham does not write his own job description. God defines the task and Abraham acts in God's behalf.
Many times we as parents buy into the world's philosophy of parenting. You are not to be your child's best friend. You are to be a parent in the authority of God. Your job is to train them up as God commanded us to do so.
Personally, I have had to scrap most 'parenting' advice because it was contrary to the Bible! If you were raised in a ungodly home, you must clean out the lies and replace them with the truth, and the truth is found in the Bible.