8. To no one owe ye, etc. There are those who think that this was not said without a taunt, as though Paul was answering the objection of those who contended that Christians were burdened in having other precepts than that of love enjoined them. And indeed I do not deny, but that it may be taken ironically, as though he conceded to those who allowed no other law but that of love, what they required, but in another sense. And yet I prefer to take the words simply as they are; for I think that Paul meant to refer the precept respecting the power of magistrates to the law of love, lest it should seem to any one too feeble; as though he had said, — “When I require you to obey princes, I require nothing more than what all the faithful ought to do, as demanded by the law of love: for if ye wish well to the good, (and not to wish this is inhuman,) ye ought to strive, that the laws and judgments may prevail, that the administrators of the laws may have an obedient people, so that through them peace may be secured to all.” He then who introduces anarchy, violates love; for what immediately follows anarchy, is the confusion of all things. ^f405

Calvin focuses on "anarchists," that is, those who believe they are not bound by any laws. His critique is impotent and misdirected. The "anarchism" espoused on this website is critical of the State precisely because it is the most powerful force for lawlessness and disorder on the planet.

Paul counsels submission to the State not because this helps the State which in turn preserves law and order. He counsels submission to the State on the same grounds he counsels submission to other evil-doers. (Romans 12:17-21)

For he who loves another, etc. Paul’s design is to reduce all the precepts of the law to love, so that we may know that we then rightly obey the commandments, when we observe the law of love, and when we refuse to undergo no burden in order to keep it. He thus fully confirms what he has commanded respecting obedience to magistrates, in which consists no small portion of love.

But some are here impeded, and they cannot well extricate themselves from this difficulty, — that Paul teaches us that the law is fulfilled when we love our neighbor, for no mention is here made of what is due to God, which ought not by any means to have been omitted. But Paul refers not to the whole law, but speaks only of what the law requires from us as to our neighbor. And it is doubtless true, that the whole law is fulfilled when we love our neighbors; for true love towards man does not flow except from the love of God, and it is its evidence, and as it were its effects. But Paul records here only the precepts of the second table, and of these only he speaks, as though he had said, — “He who loves his neighbor as himself, performs his duty towards the whole world.” Puerile then is the gloss of the Sophists, who attempt to elicit from this passage what may favor justification by works: for Paul declares not what men do or do not, but he speaks hypothetically of that which you will find nowhere accomplished. And when we say, that men are not justified by works, we deny not that the keeping of the law is true righteousness: but as no one performs it, and never has performed it, we say, that all are excluded from it, and that hence the only refuge is in the grace of Christ.

9. For this, Thou shalt not commit adultery, etc. It cannot be from this passage concluded what precepts are contained in the second table, for he subjoins at the end, and if there be any other precept. He indeed omits the command respecting the honoring of parents; and it may seem strange, that what especially belonged to his subject should have been passed by. But what if he had left it out, lest he should obscure his argument? Though I dare not to affirm this, yet I see here nothing wanting to answer the purpose he had in view, which was to show, — that since God intended nothing else by all his commandments than to teach us the duty of love, we ought by all means to strive to perform it. And yet the uncontentious reader will readily acknowledge, that Paul intended to prove, by things of a like nature, that the import of the whole law is, that love towards one another ought to be exercised by us, and that what he left to be implied is to be understood, and that is, — that obedience to magistrates is not the least thing which tends to nourish peace, to preserve brotherly love.

The Fifth Commandment ("Honor thy mother and father") is closely related to the issues of magistrates. More here.

Paul is not saying (Romans 13:1-7) that we ought to obey magistrates because this encourages brotherly love. He doesn't say (Romans 12:17-21) that we ought to submit to evil because this preserves the public peace.

• Thou shalt not kill.
• Thou shalt not steal.

Calvin was usually more in tune with the specifics of God's Law.

• WAS CALVIN A THEONOMIST?, by Gary North

Although there were exceptions:

• Nelson on Calvin, Part Two
• R. J. Rushdoony on Calvin

But Calvin misses this connection between the State and God's Law because he is more interested in buttressing the power of the State.

10. Love doeth no evil to a neighbor, etc. He demonstrates by the effect, that under the word love are contained those things which are taught us in all the commandments; for he who is endued with true love will never entertain the thought of injuring others. What else does the whole law forbid, but that we do no harm to our neighbor? This, however, ought to be applied to the present subject; for since magistrates are the guardians of peace and justice, he who desires that his own right should be secured to every one, and that all may live free from wrong, ought to defend, as far as he can, the power of magistrates. But the enemies of government show a disposition to do harm. And when he repeats that the fulfilling of the law is love, understand this, as before, of that part of the law which refers to mankind; for the first table of the law, which contains what we owe to God, is not here referred to at all.

The Law of God does more than forbid harm. The Westminster Larger Catechism rightly notes that the prohibition of something also contains a mandate of its opposite: Rules for Understanding the Commandments

Magistrates do more wrong and violate more rights than non-magistrates by several orders of magnitude.