Dionysius the Little () did not choose 25 December to stress a link with or another Jewish festival. The date of 25 December had already been set by the Church of in the 4th century, well before him. His role was above all to create a new dating system (the Anno Domini), and not to determine the festival of Christmas.
What Dionysius the Little did
A monk and scholar of the 6th century, he is known for establishing the Paschal computus (the calculation of the dates of Easter) and for proposing to date the years from the birth of Christ.
He set the Incarnation on 25 December of the year 753 since the founding of , which became Year 1 of the Christian era.
But according to some, he made a calculation error: the Messiah Jesus was born under Herod, who died, according to one interpretation of the writings of Flavius Josephus, in 750 AUC, so on this hypothesis the birth of the Messiah Jesus would probably fall between 6 and 4 BC. However, other hypotheses are considered, in particular the year 1 BC (753 AUC), which would place the birth in the year 2 BC (752 AUC). These calculations all come from interpretations of the same information provided by Flavius Josephus.
Why 25 December?
The date of 25 December had been adopted by the Church of as early as the 4th century, well before Dionysius. It reflected a desire to Christianize the pagan festival of Sol Invictus (the “Unconquered Sun”), celebrated at the winter solstice.
The choice symbolized that the Messiah Jesus is the true light of the world, coming at the moment when the days begin to lengthen.
Other Christian traditions celebrated the Nativity on 6 January (Epiphany), before 25 December became established in the West.
And what about 12 October?
Some scholars suggest that the Messiah Jesus was born at another time of year (autumn, around September–October), based on clues such as the presence of shepherds in the fields or calculations related to the priestly courses.
But there is no historical certainty about a precise date. 12 October is one hypothesis among others, with no academic consensus.
Conclusion
Dionysius the Little did not intend to stress a link with : he simply established a dating system by adopting the date of Christmas already set by the Church. 25 December is a symbolic choice tied to the solstice and to light, whereas the actual date of Jesus’s birth remains uncertain, probably a few years before the year 1 and perhaps in autumn.
In summary: Dionysius did not invent Christmas on 25 December; he only fixed the Christian calendar around this date, which had already been chosen.