According to the Catholic Church, if a Catholic's own interpretation of scripture leads to a conclusion regarding what scripture says that the Catholic Church holds is heretical (for ex., denying Trinitarianism), and this Catholic publicly says so, but he also publicly holds that the Catholic Church's position is correct, due to the authority of the Magisterium (so, he concludes that his own reasoning regarding scripture must be mistaken, as plain as it may seem to him), is he a heretic?
If a Catholic believes scripture supports a heretical position, but denies that position himself based on the Magisterium, is he a heretic?
According to the Catholic Church: Doubtful.
If ”he concludes that his own reasoning regarding Scripture must be mistaken”, then no. He should talk to a Catholic theologian to ascertain his situation, since there are nuances in the posted question that may need clarity. What translation is an individual using? ...
The Teaching Magisterium of the Catholic Church is the church's authority or office to give authentic interpretation of the Word of God, "whether in its written form or in the form of Tradition." According to the Catechism of the Catholic Church, the task of interpretation is vested uniquely in the Pope and the bishops, though the concept has a complex history of development. Scripture and Tradition "make up a single sacred deposit of the Word of God, which is entrusted to the Church", and the Magisterium is not independent of this, since "all that it proposes for belief as being divinely revealed is derived from this single deposit of faith."
To be a Catholic is to accept that the Church can not (ex cathedra) err in faith and morals.
What is heresy?
Commonly refers to a doctrinal belief held in opposition to the recognized standards of an established system of thought. Theologically it means an opinion at variance with the authorized teachings of any church, notably the Christian, and especially when this promotes separation from the main body of faithful believers.
In the Roman Catholic Church, heresy has a very specific meaning. Anyone who, after receiving baptism, while remaining nominally a Christian, pertinaciously denies or doubts any of the truths that must be believed with divine and Catholic faith is considered a heretic. Accordingly four elements must be verified to constitute formal heresy; previous valid baptism, which need not have been in the Catholic Church; external profession of still being a Christian, otherwise a person becomes an apostate; outright denial or positive doubt regarding a truth that the Catholic Church has actually proposed as revealed by God; and the disbelief must be morally culpable, where a nominal Christian refuses to accept what he knows is a doctrinal imperative.
Objectively, therefore, to become a heretic in the strict canonical sense and be excommunicated from the faithful, one must deny or question a truth that is taught not merely on the authority of the Church but on the word of God revealed in the Scriptures or sacred tradition. Subjectively a person must recognize his obligation to believe. If he acts in good faith, as with most persons brought up in non-Catholic surroundings, the heresy is only material and implies neither guilt nor sin against faith.
What is infallibility?
Freedom from error in teaching the universal Church in matters of faith or morals. As defined by the First Vatican Council, "The Roman Pontiff, when he speaks ex cathedra—that is, when in discharge of the office of pastor and teacher of all Christians, by virtue of his supreme apostolic authority, he defines a doctrine regarding faith or morals to be held by the universal Church, by the divine assistance promised to him in Blessed Peter, is possessed of that infallibility with which the divine Redeemer willed that his Church should be endowed in defining doctrine regarding faith or morals; and therefore such definitions are irreformable of themselves, and not in virtue of consent of the Church" (Denzinger 3074).
The bearer of the infallibility is every lawful Pope as successor of Peter, the Prince of the Apostles. But the Pope alone is infallible, not others to whom he delegates a part of his teaching authority, for example, the Roman congregations.
The object of his infallibility is his teaching of faith and morals. This means especially revealed doctrine like the Incarnation. But it also includes any nonrevealed teaching that is in any way connected with revelation.
The condition of the infallibility is that the Pope speaks ex cathedra. For this is required that: 1. he have the intention of declaring something unchangeably true; and 2. he speak as shepherd and teacher of all the faithful with the full weight of his apostolic authority, and not merely as a private theologian or even merely for the people of Rome or some particular segment of the Church of God.
The source of the infallibility is the supernatural assistance of the Holy Spirit, who protects the supreme teacher of the Church from error and therefore from misleading the people of God.
As a result, the ex cathedra pronouncements of the Pope are unchangeable "of themselves," that is, not because others in the Church either first instructed the Pope or agree to what he says.
Wikipedia can sum it up essentially easy enough.
Heresy in the Catholic Church denotes the formal denial or doubt of a core doctrine of the Roman Catholic Church. Heresy has a very specific meaning in the Catholic Church and there are four elements which constitute formal heresy; a valid Christian baptism; a profession of still being a Christian; outright denial or positive doubt regarding a truth that the Catholic Church regards as revealed by God; and lastly, the disbelief must be morally culpable, that is, there must be a refusal to accept what is known to be a doctrinal imperative. Therefore, to become a heretic in the strict canonical sense and be excommunicated, one must deny or question a truth that is taught as the word of God, and at the same time recognize one's obligation to believe it. If the person is believed to have acted in good faith, as one might out of ignorance, then the heresy is only material and implies neither guilt nor sin against faith.
How should we as Catholics interpret Scriptures, in order to avoid errors? Personal interpretation, in the eyes of the Church is at times a dangerous enterprise, especially when we take into consideration the vast number of biblical translations out there. Many are not close to the actual Koine Greek at all.
Bible interpretation results in a wide spectrum of belief in modern-day Christianity, making it difficult to know who is right and where to search for reliable answers. In the Catholic Church, there are specific guidelines to follow to ensure a correct reading of the Bible that is faithful to its original intention and consistent with Christian belief.
The Compendium of the Catechism of the Catholic Church offers an introductory explanation of how a Catholic is to interpret the Bible.
Sacred Scripture must be read and interpreted with the help of the Holy Spirit and under the guidance of the Magisterium of the Church according to three criteria: 1) it must be read with attention to the content and unity of the whole of Scripture; 2) it must be read within the living Tradition of the Church; 3) it must be read with attention to the analogy of faith, that is, the inner harmony which exists among the truths of the faith themselves.
These are broad, sweeping guidelines can be difficult to understand. The primary purpose of these guidelines is to explain how we shouldn’t succumb to the temptation to take a particular scripture passage out of context, or without consulting the history and tradition of the Church.
The Church doesn't correct Holy Scripture's errors because it contains none. The Church has already dogmatically defined which books are part of the canon of Holy Scripture and thus are the inerrant Word of God.
One publicly states [what one thinks is] […] [a correct] reading [interpretation of Holy Scripture], but also states one goes with the Magisterium, and so something must be wrong with one's own reading.
It sounds like you mean how St. Thomas Aquinas structures his Summa Theologica articles: objections followed by answers. The objections are seemingly valid arguments, often based off Scriptural verses, but they contain some errors, which are corrected in the replies.