Swearing oaths
Whether oaths are forbidden altogether or only their misuse, since the law itself commands swearing by the Name.
Matthew 5:33-37
33“Again you have heard that it was said to the ancient ones, ‘You shall not make false vows, but shall perform to the Lord your vows,’
34but I tell you, don’t swear at all: neither by heaven, for it is the throne of God;
35nor by the earth, for it is the footstool of his feet; nor by Jerusalem, for it is the city of the great King.
36Neither shall you swear by your head, for you can’t make one hair white or black.
37But let your ‘Yes’ be ‘Yes’ and your ‘No’ be ‘No.’ Whatever is more than these is of the evil one.
Deuteronomy 6:13
13You shall fear Yahweh your God; and you shall serve him, and shall swear by his name.
What each tradition says
Rabbinic / Midrashic
Rashi reads Deuteronomy 6:13 as permitting an oath by God's name only for one who reveres His name and serves Him. Such reverence makes a person cautious with the oath. Without those characteristics, one must not swear by His name.
Rashi (R. Solomon ben Isaac), Rashi on Deuteronomy 6:13 — Pentateuch with Rashi's commentary by M. Rosenbaum and A.M. Silbermann (1929-1934), served by Sefaria — Commentary on Deuteronomy 6:13
Patristic
John Chrysostom affirms that swearing is altogether of the evil one now, after so high a rule of self-restraint. Yet he adds that then it was not so.
John Chrysostom, Homilies on the Gospel of St. Matthew (Nicene and Post-Nicene Fathers, First Series, Vol. 10; George Prevost trans.) — Homily 17 (on Matthew 5:33-37)
Catholic
Aquinas holds that swearing is not evil in itself; when necessity forces it, one makes good use of swearing to persuade another to a useful purpose. The evil is not something over and above, but comes from the infirmity of the person one must convince.
Thomas Aquinas, Summa Theologiae (Fathers of the English Dominican Province trans., second and revised edition) — II-II, q. 89, a. 1, ad 2
Orthodox
Philaret notes that men swear by the greater, and God confirmed it by an oath to show the heirs of promise the immutability of his counsel. He concludes that if God used an oath, much more may we, on grave and necessary occasions, when required by lawful authority, take an oath or vow religiously, intending not to break it.
Philaret of Moscow, The Longer Catechism of the Orthodox, Catholic, Eastern Church (R.W. Blackmore trans.; in Schaff, Creeds of Christendom) — Part III, Q. 535 (On the Third Commandment)
Reformed / Protestant
Calvin reads Jesus’ command “swear not at all” as addressing the form or manner of swearing, not its substance. The prohibition means swearing neither directly nor indirectly, whether by heaven or by earth, to meet the crime being addressed.
John Calvin, John Calvin's Bible Commentary (Calvin Translation Society) — On Matthew 5:34
Evangelical
John Wesley’s note states that Jesus corrects a false doctrine of the scribes arising from not seeing God in all things. He forbids swearing at all, by any creature, in ordinary conversation, which the scribes and Pharisees taught was perfectly innocent.
John Wesley, Explanatory Notes upon the New Testament — Note on Matthew 5:33