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Why is denial of the primacy of the bishop of Rome considered a Schism, not a Heresy?
Disclaimer: I'm interesting only in authoritative answer according to the Roman Catholic Doctrine.
The Papal primacy is essentially dogma of Roman Catholic Church. So why are those who deny this dogma (say, Orthodox Church officials) not formally considered as heretics?
According to Canon law, it is technically both:
Can. 751 Heresy is the obstinate denial or obstinate doubt after the reception of baptism of some truth which is to be believed by divine and Catholic faith; apostasy is the total repudiation of the Christian faith; schism is the refusal of submission to the Supreme Pontiff or of communion with the members of the Church subject to him. - Code of Canon Law
However, an arguable effect of JOINT CATHOLIC-ORTHODOX DECLARATION OF HIS HOLINESS POPE PAUL VI AND THE ECUMENICAL PATRIARCH ATHENAGORAS I is that it is no longer appropriate to affix the label "heretic" across the schismatic divide:
...in common agreement, declare that:
...
B. They likewise regret and remove both from memory and from the midst of the Church the sentences of excommunication which followed these events, the memory of which has influenced actions up to our day and has hindered closer relations in charity; and they commit these excommunications to oblivion. [emphasis added]
St. Thomas Aquinas answers this well in Summa Theologica II-II q. 39 a. 1 ("Whether schism is a special sin?") ad 3:
…heresy is essentially opposed to faith, while schism is essentially opposed to the unity of ecclesiastical charity. Wherefore just as faith and charity are different virtues, although whoever lacks faith lacks charity, so too schism and heresy are different vices, although whoever is a heretic is also a schismatic, but not conversely. This is what Jerome says in his commentary on the Epistle to the Galatians [In Ep. ad Tit. iii, 10]:
I consider the difference between schism and heresy to be that heresy holds false doctrine while schism severs a man from the Church.Nevertheless, just as the loss of charity is the road to the loss of faith, according to 1 Tim. 1:6: "From which things," i.e. charity and the like, "some going astray, are turned aside into vain babbling," so too, schism is the road to heresy. Wherefore Jerome adds (In Ep. ad Tit. iii, 10) thatat the outset it is possible, in a certain respect, to find a difference between schism and heresy: yet there is no schism that does not devise some heresy for itself, that it may appear to have had a reason for separating from the Church.
Refusal of submission to the Bishop of Rome is schism, not heresy, because the nature of schism and heresy are different.
Heresy always entails proposing a false doctrine, or else denying or (expressly and persistently) doubting the truth of a doctrine that must be believed. As other posters have pointed out, the Code of Canon Law defines heresy as
the obstinate denial or obstinate doubt after the reception of baptism of some truth which is to be believed by divine and Catholic faith (Can. 751).
Schism, on the other hand, means a wilful separation from the Church:
schism is the refusal of submission to the Supreme Pontiff or of communion with the members of the Church subject to him (ibid.).
Schism does not necessarily entail false doctrine or the denial (or doubt) of true doctrine; therefore, it does not necessarily imply heresy.
For example, most sedevacantist groups (those who deny that the current Pope is legitimate) do not deny that there is a Petrine office (which would be a heresy); they merely say that the current claimant to that office is illegitimate.
It should be observed, regarding heresy, that a distinction should be made between material heresy and formal heresy. The former occurs whenever someone affirms a doctrine that, objectively speaking, is false (contrary to a doctrine that must be held with divine and Catholic faith), or else denies or doubts one that is true.
Formal heresy, however, only occurs when this affirmation, denial, or doubt is wilful.
For example, I think it is unlikely that the vast majority of Protestants have committed formal heresy, even though Catholics would consider some of the doctrines they affirm to be materially heretical.
The Catholic Church would consider a member of the Eastern Orthodox Church who denies the primacy of the Bishop of Rome (which would be a material heresy) in a similar light.
Having said that, the Eastern Orthodox Church remains fully orthodox in essentially all of the most fundamental doctrines (Trinitarian theology*, Christology, sacraments, etc.). For this reason the situation of the Eastern Orthodox Church is, from the Catholic Church’s perspective, more schismatic than (materially) heretical.
Note that, in order for a person to incur the censure of heresy or schism (which is what this canon contemplates), he must be formally a member of the Catholic Church. That does not apply, evidently, either to Protestants or to the Orthodox.
* The Catholic Church considers the Eastern Orthodox fully orthodox in Trinitarian theology, notwithstanding the controversy over the Filioque. Regarding this, I suggest reading my answer to the question What are the theological implications of “filioque”?, which explains more fully.
