No… that’s not my conclusion.
My conclusion is that they wanted to establish Jesus as having equally reasonable credentials to be celebrated in connection with December 25.
Over the course of centuries, this enabled December 25 to be replaced by a Christian celebration.
You act as if nobody would ever want Jesus connected with some pagan notion. But the whole idea of resurrection connects Jesus with many forms of Paganism, right?
The story of the the disuse of the term Pontifex Maximus - - and then re-use of the term by the Pope - - is a perfectly fine demonstration of the desire to connect Christianity with important symbols of Paganism, and in so doing, eventually eliminate the pagan connection in future generations of the popular audience!
From the time of Theodosius I (r 379–395), the emperors no longer appear in the dignity of pontiff, but the title was later applied to the Christian bishop of Rome.
In 382, the Emperor Gratian, at the urging of Ambrose, removed the Altar of Victory from the Forum, withdrew the state subsidies that funded many pagan activities and formally renounced the title of Pontifex Maximus.[40: “In the latter part of his reign Gratian was greatly influenced by St. Ambrose. Out of deference to the Christian church, he omitted the words pontifex maximus (“supreme priest”) from his title—the first Roman ruler to do so—and ordered the removal of the pagan statue of Victory from the Senate in Rome. An embassy of the senators, led by Quintus Aurelius Symmachus, failed to persuade him to rescind his instructions on this matter.” https://www.britannica.com/biography/Gratian-Roman-emperor#ref110357 ]
In one of the more even-handed discussions of the Pagan term, we read the following:
“The last traces of emperors being at the same time chief pontiffs are found in inscriptions of Valentinian, Valens, and Gratianus (Orelli, Inscript. n1117, 1118). From the time of Theodosius I (379–395), the emperors no longer appear in the dignity of pontiff…”
"It is said that Pope Damasus I was the first Bishop of Rome to assume the title
[FN17: “[per] Mark Bonocore Retrieved February 15, 2009. This seems to be based on the Theodosian Code, XVI.i.2, which refers to Pope Damasus merely as a pontifex, not as the pontifex maximus. The Christian Apostolic Succession, The Role and Function of Thelemic Clergy in Ecclesia Gnostica Catholica, Retrieved February 15, 2009. states that Damasus refers to himself as Pontifex Maximus in a petition to the Emperor for judicial immunity, but gives no source for this statement.”],
"…other sources say that the use of such titles by bishops, including the Bishop of Rome, came later.
[FN18: ““Christian emperors relinquished the title Pontifex Maximus as too closely tied with the pagan past (Schimmelpfennig, 34). Bishops, including the bishop of Rome, sometime thereafter, began to make use of pontifex as a title for themselves” (John D. Beetham, Papal Prerogatives and Titles, 5 September 2001 (emphasis added). Retrieved February 15, 2009.”]
"The title pontifex continued to be a title for both the bishop of Rome and other bishops. In Emperor Theodosius’s edict De fide catholica [FN19: De Fide Catholica, per https://droitromain.univ-grenoble-alpes.fr/ ]
. . . of February 27, 380, enacted in Thessalonica and published in Constantinople for the whole empire, by which he established Catholic Christianity as the official religion of the empire, he referred to Damasus as a pontifex,
[FN20: “Unlike episcopus (from Greek ἐπίσκοπος), the word used for the bishop from the Greek-speaking East, pontifex is a word of purely Latin derivation. Retrieved February 15, 2009.” ]
. . . . while calling Peter an episcopus : “… the profession of that religion which was delivered to the Romans by the divine Apostle Peter, as it has been preserved by faithful tradition and which is now professed by the Pontiff Damasus and by Peter, Bishop of Alexandria … We authorize the followers of this law to assume the title Catholic Christians …”
Some see in this an implied significant differentiation, but the title pontifex maximus is not used in the text; pontifex is used instead: “… quamque pontificem damasum sequi claret et petrum alexandriae episcopum…” (Theodosian Code XVI.1.2; and Sozomen, “Ecclesiastical History,” VII, iv. [FN21: Emperor Theodosius I. “IMPERATORIS THEODOSIANI CODEX Liber Decimus Sextus” (web http://ancientrome.ru/ius/library/codex/theod/liber16.htm). Retrieved 2006-12-04. Retrieved February 15, 2009.])."
@Jonathan_Burke, I would think you would be more embarassed on behalf of the Church, to suggest that these early apologists genuinely thought Jesus was born in December - - rather than to give them the most plausible of denials - - that they wanted to make sure that Pagan audiences would not see Jesus as deficient in terms of gravitas that was otherwise provided to other pagan celebrations of the Winter Solstice.