Who, in the Roman Catholic Church has declared that Matthew 16:18 teaches empowerment of the Magesterium with inerrancy regarding faith and morals?

The Catholic Church does not claim that Matthew 16:18-19 is empowering the Magisterium. Rather, the Magisterium is empowered by Christ.

See the Catechism of the Catholic Church (emphasis mine):

"How are they to believe in him of whom they have never heard? And how are they to hear without a preacher? And how can men preach unless they are sent?" No one - no individual and no community - can proclaim the Gospel to himself: "Faith comes from what is heard." No one can give himself the mandate and the mission to proclaim the Gospel. The one sent by the Lord does not speak and act on his own authority, but by virtue of Christ's authority; not as a member of the community, but speaking to it in the name of Christ. No one can bestow grace on himself; it must be given and offered. This fact presupposes ministers of grace, authorized and empowered by Christ. From him, bishops and priests receive the mission and faculty ("the sacred power") to act in persona Christi Capitis; deacons receive the strength to serve the people of God in the diaconia of liturgy, word and charity, in communion with the bishop and his presbyterate. The ministry in which Christ's emissaries do and give by God's grace what they cannot do and give by their own powers, is called a "sacrament" by the Church's tradition. Indeed, the ministry of the Church is conferred by a special sacrament. (CCC 875)

The Church sees evidence in Scripture that the presbyterate has authority to teach:

Do not neglect the gift you have, which was conferred on you through the prophetic word with the imposition of hands of the presbyterate. Be diligent in these matters, be absorbed in them, so that your progress may be evident to everyone. Attend to yourself and to your teaching; persevere in both tasks, for by doing so you will save both yourself and those who listen to you. (1 Timothy 4:14-6)

And that these presbyters have been appointed by others who have been given the authority to do so:

For this reason I left you in Crete so that you might set right what remains to be done and appoint presbyters in every town, as I directed you. (Ti 1:5)

But this evidence is not the cause of nor reason for the Church's authority to teach. It is, rather, an example of that authority in action.

Who, in the Roman Catholic Church has declared that Matthew 16:18 teaches empowerment of the Magesterium with inerrancy regarding faith and morals?

18 And I say to thee: That thou art Peter; and upon this rock I will build my church, and the gates of hell shall not prevail against it.

19 And I will give to thee the keys of the kingdom of heaven. And whatsoever thou shalt bind upon earth, it shall be bound also in heaven: and whatsoever thou shalt loose upon earth, it shall be loosed also in heaven. - Matthew 16:18-19

Before going on with an explication, let us take a look as to what the Church explains what exactly is the Church’s Magisterium.

Magisterium

The Church's teaching authority, vested in the bishops, as successors of the Apostles, under the Roman Pontiff, as successor of St. Peter. Also vested in the Pope, as Vicar of Christ and visible head of the Catholic Church. (Etym. Latin magister, master.)

Not to confident anyone in the Catholic Church has declared that Matthew 16:18 teaches empowerment of the Magesterium with inerrancy regarding faith and morals!

Even the doctrine of Papal Infallibility extends only to the person of the pope when speaking infallibly on matters of faith and morals and then only when he pronounces such statements ex cathedra. The Teaching Magisterium can not do this on it’s own.

Papal infallibility is a dogma of the Roman Catholic Church which states that, in virtue of the promise of Jesus to Peter, the pope when he speaks ex cathedra is preserved from the possibility of error on doctrine "initially given to the apostolic Church and handed down in Scripture and tradition".

This doctrine was defined dogmatically at the First Vatican Council of 1869–1870 in the document Pastor aeternus; this doctrine had been defended before that, and it is claimed it already existed in medieval theology; this doctrine was the majority opinion at the time of the Counter-Reformation.

The doctrine of infallibility relies on one of the cornerstones of Catholic dogma: that of papal supremacy, and his authority as the ruling agent who decides what are accepted as formal beliefs in the Roman Catholic Church. The use of this power is referred to as speaking ex cathedra. “Any doctrine 'of faith or morals' issued by the pope in his capacity as successor to St. Peter, speaking as pastor and teacher of the universal church, from the seat of his episcopal authority in Rome, and meant to be believed 'by the universal church,' has the special status of an ex cathedra statement. Vatican Council I in 1870 declared that any such ex cathedra doctrines have the character of infaillibility (session 4, Constitution on the Church 4)." The doctrine of the Immaculate Conception proclaimed by Ineffabilis Deus in 1854 is "generally accepted" as being an ex cathedra statement. Since the declaration of papal infallibility by Vatican I (1870), the only example of an ex cathedra statement thereafter took place in 1950, when Pope Pius XII defined the Assumption of Mary as an article of faith. In Ineffabilis Deus and Pius XII's cases, the popes consulted with Catholic bishops before making their declaration.

When he was prefect of the Congregation for the Doctrine of the Faith, Cardinal Ratzinger (later Pope Benedict XVI), under John Paul II's authority, stated in a formal response (responsum) to an inquiry (dubium) that John Paul II's decision on the ordination of women into the Catholic priesthood in his apostolic letter Ordinatio sacerdotalis was part of the "ordinary and infallible" magisterial teaching of the Catholic Church. Prof. Frank K. Flinn claims that Pope John Paul II's statement on the inadmissibility of women to the priesthood was not infallible; Kilnn considers that Cardinal Ratzinger's later responsa to the dubium on the subject was therefore erroneous. Pope Francis stated in an interview that John Paul II's decision was "[t]he final word" on women ordination.

Conditions for teachings being declared infallible

According to the teaching of the First Vatican Council and Catholic tradition, the conditions required for ex cathedra papal teaching are as follows:

• the Roman Pontiff (the Pope alone or with the College of Bishops)

• speaks ex cathedra, that is, when, (in the discharge of his office as shepherd and teacher of all Christians, and by virtue of his supreme apostolic authority,) he defines a doctrine

1. concerning faith or moral

2. to be held by the whole Church.

The terminology of a definitive decree usually makes clear that this last condition is fulfilled, as through a formula such as "By the authority of Our Lord Jesus Christ and of the Blessed Apostles Peter and Paul, and by Our own authority, We declare, pronounce and define the doctrine . . . to be revealed by God and as such to be firmly and immutably held by all the faithful," or through an accompanying anathema stating that anyone who deliberately dissents is outside the Catholic Church.

For example, in 1950, with Munificentissimus Deus, Pope Pius XII's infallible definition regarding the Assumption of Mary, there are attached these words: "Hence if anyone, which God forbid, should dare willfully to deny or to call into doubt that which We have defined, let him know that he has fallen away completely from the divine and Catholic Faith."

As with all charisms, the church teaches that the charism of papal infallibility must be properly discerned, though only by the Church's leaders. The way to know if something a pope says is infallible or not is to discern if they are ex cathedra teachings. Also considered infallible are the teachings of the whole body of bishops of the Church, especially but not only in an ecumenical council.

Thus it is obvious that the Teaching Magisterium is not empowered with inerrancy regarding faith and morals, according to Matthew 16:18-19! The Magisterium can only teach that which the Catholic Church has already professed and defined by the pope and those bishops united to the Supreme Pontiff. The Teaching Magisterium can not define new doctrines on its own. Papal Infallibility extends to the person of pope.