All of us have a relationship to authority. The question is what the nature of that relationship is. From the time that your mother Eve reached out her hand and gave to her husband to eat, all of their children have desired the same autonomy (literally, self-law). For Christians though, the relationship is different. Christians can and should submit to the ordained civil authorities as free servants of God.
But if you read the text closely, the verb is reflexive. That is, it is something that you do to yourself. The civil magistrate should not have to compel you to submit. Having said this, the Scriptures say that you are to submit to every "ordinance of man" which means that the magistrate has authority only in those matters that are common to mankind. He does not have the authority to command your conscience, dictate the content of preaching and worship, nor any other matter that is outside his area of responsibility. In that case, the Christian has the right and responsibility to resist that kind of tyranny. Nevertheless, the Christian's submission to the civil power is an active responsibility for the Lord's sake. The Lord is Lord of all, and resistance and rebellion to lawful and ordained human authority is resistance and rebellion against God's order.
The text is explicit that submission to the magistrate is submission to the will of God. It is also explicit that the submission to the civil power is a means of silencing the ignorant fools who blaspheme the Faith and the Lord. Think of the times in which Peter wrote these words. Christians were viewed with great suspicion. Very early on, they were called atheists because they did not believe in all of the gods of Rome. They would be called traitors because they did not worship the emperor. They were accused of incest because they called one another brother and sister, and they were accused of sexual looseness and cannibalism because of the Lord's Supper and the associated Love-feasts. Yet, in the midst of all this slander, as free servants of God, we are to obey when and where we can because the Lord in Heaven is Lord of all and because the Kingdom of God is advanced.
Speaking of submission, in verse 17 the apostle turns his attention toward the basic duties in a quick summary. Our relationship to all humankind is one of honor, but to the brotherhood of faith we have a further responsibility to love. You ought to discriminate between those of the household of faith and those who are outside. Your brothers and sisters in the faith have a greater demand upon your affections, gifts, time and property than unbelievers do. And above all, you are to reverently fear God who is Lord of all. Honor the magistrate, but fear God. There may come a time when we must resist the tyranny of the civil power, but the normal relationship is, "tribute to whom tribute is due; custom to whom custom; fear to whom fear; honor to whom honor." (Romans 13:7)