Because a large amount of RC teaching is on the premise of the existence of purgatory, such as penance and indulgences.
Well, that’s true. However, we would not say that these teaching are based on the premise of the existence of Purgatory as much as they (along with Purgatory) are based on the Apostolic and Biblical principals of how Christian salvation operates, i.e., how both the righteousness of Christ (justification) and the holiness of Christ (sanctification) are truly and substantially shared with the Christian in the context of an intimate and loving Covenant, not merely imputed in a legalistic way. This is the essential difference between Catholicism and Lutheranism.
Lutheranism takes a legalistic approach to salvation, casting God in the role of our Judge. Catholicism, while it of course acknowledges that God is our Judge, upholds the more basic and Apostolic view of God as our Father (understanding that He is only our Judge in a Fatherly capacity). As if it even needs to be pointed out, a Father obviously requires more from His son (or daughter) than a CIVIL Judge requires from a citizen. A Father requires that His child not only obey His laws, but that His child take them to heart and truly be righteous, even as He Himself is Righteous, i.e., Covenantal intimacy. Lutheranism does not require this. Indeed, it makes it irrelevant; and so distorts the very nature and meaning of a Covenant, an “exchange of persons.” It reduces our Covenant with and in Christ to a mere legalistic “contract.” This is why the Catholic Church must reject imputed justification as an error.
Plus, purgatory was only made doctrine at the council of Trent in the 16th century, and the doctrine that it became did not resemble what the early church fathers referred to as a state of purification.

I’m very sorry, but you are grossly mistaken about that. Your first misunderstanding is that you confuse the term “doctrine” with “dogma.” A “doctrine” is a general teaching of the Church, which may be officially binding and an essential element of Apostolic Tradition, or it may be what is called a “
theologoumenon” (a “theological opinion”), which is not necessarily binding and can be debated among Catholics. A “dogma,” on the other hand, is a formally binding teaching of the Church, e.g. the Trinity as defined by the Council of Nicaea. It should be noted that all dogmas start out as “theological opinions” and may be debated and refined until the Church speaks formally and declares a particular position to be a dogma. This is what happened at the Council of Trent - but only when it came to the specific Protestant objections to Purgatory.
However, Purgatory itself was dogmatized by earlier Councils, such as the Council of Ferrara-Florence (c. 1439), which preceded Trent, and which addressed, not Protestant objections to Purgatory, but the differences between the Western / Latin approaches to the mystery we called “Purgatory” and the Eastern / Greek approaches to this very same mystery. So, Purgatory was a formally declared dogma for over a century before the Council of Trent.
What also needs to be appreciated is that the Church almost never declares a particular doctrine to be a dogma unless or until it is threatened by some heretical challenge. This, again, is why Purgatory was defined as a dogma at Ferrara-Florence and at Trent, i.e., in response to Greek and to Protestant challenges, respectively. However, as with other Traditional doctrines which were not formally dogmatized until they were challenged, Purgatory was always universally appreciated by the Church since earliest times, and was part of the Apostolic Deposit of Faith. This is very clear in the writings of the early Church fathers (see below).
As I said, the only reason why the Church normally defines something clearly as a binding dogma is when that element of the Faith is challenged by a heresy. Until that happens, the Church is very happy to observe such beliefs in undefined and organic forms, just as it did with its understanding of the Trinity (before the Church was forced to clearly and dogmatically define its organic understanding, in response to the Arian heretics, at the Council of Nicaea in A.D. 325 and the Council of Constantinople I in A.D. 381), and just as it did with its understanding of the Hypostatic Union of Christ (before the Church was forced to clearly and dogmatically define its organic understanding, in response to the Nestorian and Monophysite heretics, at the Council of Ephesus in A.D. 431 and the Council of Chalcedon in A.D. 451). Before this time, the Church of course believed in the Trinity and in the Hypostatic Union of Christ, but it believed in them in an organic form; i.e., it possessed a deep and comprehensive understanding; but this understanding was not yet in a form where it could be clearly encapsulated into a simple explanation or articulated clearly and unambiguously so that everyone in the Church possessed the same semantic approach. This is what a dogmatic statement does: it takes the comprehensive, organic understanding of the Church and reduces it to a clear and pointed statement which can end a debate and which is binding on all.
So, when it comes to Purgatory, it is very clear that the Church always and universally possessed an organic belief in the doctrine, even if it was not always expressed using the same, specific terms or concepts. Also, what cannot be denied is that Luther’s denial of Purgatory (no matter how the mystery is approached) is totally alien to the early Church. This is because, once again, Luther introduced a 16th Century novelty which is incomparable with ancient, Apostolic Christianity.
continued. . .