Two subjects are covered here, obedience to government and loving others. We are told that God has appointed governments for our good. There are times when governments go beyond what God has appointed them to do, but when they are punishing wrongdoers, they are God’s instruments for helping people to live better lives. Since we are commanded to love others, Paul sees love as a debt we owe everyone.
Maybe one of the hardest instructions here is to respect those in authority. Freedom of speech gives people the right to express their views, but loving others requires us do so respectfully, even when we strongly disagree.