Church teachings whether infallibly true or authoritatively true are proposed to be held as true by the faithful.
So what does this mean?
Some Catholic teachings are dogma. That means they are held to be irreformally true, that is infallibly true. They are divinely revealed and are defined by an ecumenical council or the Pope speaking ex cathedra. This the Extraordinary and Solemn path of magisterial action. Dogma can also be revealed in the ordinary and non-solemn action of the bishops in union with the Pope. As Lumen Gentium says:
Although the bishops individually do not enjoy the prerogative of infallibility, they nevertheless proclaim the teaching of Christ infallibly, even when they are dispersed throughout the world, provided that they remain in communion with each other and with the successor of Peter and that in authoritatively teaching on a matter of faith and morals they agree in one judgment as that to be held definitively.Doctrine which is not divinely reveal may also be Extraordinary and Solemn. Such truths are revealed by the Holy Spirit and are typically inimately linked with revealed truths. Such truths make up Definitive Doctrine.
The rest may be said to reside under the heading of Authentic Doctrine. These truths are reformable in the light of the formation of faith, but are still authoritative, that is they must be adhered to by the faithful.
None of this was controversial at all until the post Vatican II period, specifically after July 25, 1986. What happen then? Pope Paul VI promalgated Humanae Vitae which did nothing but confirm traditional Catholic teaching on abortion and contraception.
100 theologians, among them Fr. Charles E. Curran, who was then a professor at Catholic University of America, issued a statement claiming that Catholic's individual consciences can prevail over non-dogmatic teaching, effectively rendering Authentic Doctrine meaningless. At the same time the Canadian Conference of Catholic Bishops issued the infamous Winnipeg Statement, which effectively said that Catholics were free to dissent from the teachings of the Church based on their own consciences.
This is not the teaching of the Catholic Church, though some theologians continue to support it. This has been addressed by the Congregation of the Doctrine of the Faith. The CDF holds that while theologians may question the content of proposed authoritative teachings in the pursuit of their vocation, such views are publish only so that they may be may be reviewed by their peers for submission to those within the Church who have the authority and responsibility under the magisterium to discern such doctrine. At no time are the faithful free to accept such proposed positions if they conflict with the present Authentic Doctrine as taught by the Church. Holding any other position is contrary to the Obsequium, that is the submission of will and intellect required for Authentic Doctrine.