Jesus is not banning the vows and oaths. The saying is idiomatic that instructs "make no oath at all"; it is instructed relatively to a negative that is breaking oaths, being dishonest and untrustworthy, like all other similar sayings in the Sermon on the mount such about anger, adultery, gouging your eye, divorce, not resisting the evil, loving your enemy, and hating your family (Luke 14:26) etc. These are idiomatic and hyperbolic in nature. The goal is to be perfect, as your father is perfect (Matt 5:48). Better to take no oath at all and be truthful, than to be habitual of taking oaths and even breaking them, because nobody trusts you.
[NASB Matt 23:6-10] "They love the place of honor at banquets and the chief seats in the synagogues, and respectful greetings in the market places, and being called Rabbi by men. "But do not be called Rabbi; for One is your Teacher, and you are all brothers. "Do not call [anyone] on earth your father; for One is your Father, He who is in heaven. "Do not be called leaders; for One is your Leader, [that is], Christ.
[NASB Matt 12:7]"But if you had known what this means, 'I DESIRE COMPASSION, AND NOT A SACRIFICE,' you would not have condemned the innocent.
[NASB Mic 6:6-8] With what shall I come to the LORD [And] bow myself before the God on high? Shall I come to Him with burnt offerings, With yearling calves? Does the LORD take delight in thousands of rams, In ten thousand rivers of oil? Shall I present my firstborn [for] my rebellious acts, The fruit of my body for the sin of my soul? He has told you, O man, what is good; And what does the LORD require of you But to do justice, to love kindness, And to walk humbly with your God?
It does not mean that he is banning the nouns of father, leader, Rabbi, teacher for anyone but the wrongful use of them. It is better to walk humbly with justice and righteousness than to transgress and offer reparation to correct the wrongdoing. The new covenant does not prohibit some Jewish customs and rituals, so Paul's vow was not contrary to the law of the new covenant. I will quote David Stern's Jewish NT commentary on Acts 18:18 to show some context, despite the fact his understanding of the grace and Mosaic law is off, like all other commentators:
Sha'ul remained for some time. Except where his own life was in
immediate peril Sha'ul never left at a lime of crisis or under duress.
Having his hair cut short in Cenchrea because he had taken a vow, and
with him were Priscilla and Aquila. Pnscilla is mentioned first; she
may have been the more notable of the couple. Some suggest, and the
Greek text allows, that it was Aquila and not Sha'ul who took the vow;
but since the overall narrative is about Sha'ul, this is unlikely.
Yeshua rules out oaths for Messianic believers (Mt 5:33-37) but not
vows, although the distinction beiween them is not a clear one (see Mt
5:33N). The Greek word for "vow" occurs only here and at 21:23. What
kind of vow did Sha'ul take, and what did cutting his hair have to do
with it? Nothing is said of what he vowed to do, but Numbers 6:1-21
describes the Nazirite vow, which involves allowing the hair to grow
during the days of the vow; and Mishna tractate Nazir spells out the
details of such vows, including their minimum length, thirty days.
Strictly speaking, however, this cannot have been a Nazirite vow; for
if it had been, Sha'ul would not have been shaved in Cenchrea but
would have waited till he arrived in Yerushalayim (v. 22) to shave his
head and offer the obligatory sacrifice at the Temple (compare
2I:23-24&NN). Furthermore, if we assume that the patterns described in
the Mishna, compiled around 220 C.E., were already being followed in
Sha'ul's time, he would have had to spend at least thirty days in
Israel to validate his vow (Nazir 3:6, 7:3), since a Nazirite vow
undertaken in a "land of the Gentiles" is invalid. Perhaps this was a
Diaspora adaptation of the Nazirite vow.
No matter what the details of Sha'ul's vow were, this verse proves
that he did not abandon the Torah; on the contrary, even when he
became as a Gentile among Gentiles he continued to observe Jewish
practices. See 13:9N, 1С 9:20-22&NN.