Yule was never a Roman holiday.
I'm aware, I'm addressing that people have connected Christmas to both Roman holidays of the time and Yule in this thread.
I've not seen any sources that trees were part of Yule that are not from many centuries after the relevant time period. Twigs used for fire, yes, but not trees or logs.
Is that at the time you are talking, the medical wisdom of the day held that pregnancy lasted 10 months, not 9. So there is a whiff of anachronistic error there by whoever proposed this tale.
'Medical wisdom' would vary by location and people group - it's anachronistic to claim they'd all have the same idea at the time. I've not seen Jewish sources - the sources used to determine the dates for Easter and where the concept where Moses, David, and others had 'perfect lives' - of that time that has pregnancy being 10 months.
We have many of the writings of church fathers, and many of those have fairly decent translations. We know they wanted to develop a calendar to be independent from Jewish leaders, and a significant part for them was determining when Jesus was executed. There were two dates calculated, and Christmas was calculated from those dates.
As Christianity gained power, it erased the pagan roots of what it did adopt all the better to repress and persecute out if existence the pagan customs it rejected.
That idea comes from the Victorians. It entirely erases how Christianity developed out of Judaism. Ancient Judaism has monolatry that likely developed out of a Divine Council model common in West Asia that King Josiah attempted to squash though not fully from the texts (see the god of Israel fighting the god of Moab), but that's irrelevant to connecting it to entirely different polytheistic groups (and using the pagan would be anachronistic for the time period the dates for Christmas was being developed).
Like I said, I get people find the stealing from pagan story more compelling. I'm not Christian, I don't even celebrate these holidays, I just have a background in these texts, and the answer to the OP's question about why people today make that link is that some Victorian elites pushed the idea that everything Christian is pagan. Some will always argue they did so with good reason, I don't buy it.
This isn’t exactly true. Matching local pagan customs to Christian events was often used to swell conversions by Christian missionaries when Christianity was new to a region and not yet powerful.
While not powerful in the region, they still only did that after they had power - they weren't doing that in 1st to early 3rd century CE when the development of celebrations of remembrance of his death and birth and other aspects were developed within. They only start gaining enough power in the late 3rd into the 4th century CE to start throwing any tactics like that around.
Even at the height of their power and their most violent, the Catholic church couldn't erase that they altered the dates for the festival of the dead in mid-southern part of what is now Mexico from August to November & how they synergised with the local polytheistic traditions. If they couldn't do it then, how would they when they had fuckall power and many people openly mocked the entire concept (one of the earliest depictions of the crucifixion is graffiti mocking the concept of worshipping someone crucified). That was the environment the dates were calculated and developed in, an environment where if they had tried to co-opt Roman or any other known holidays, we'd likely have sources mocking them for it as we have for other things they did or that they suffered violence for it (it could be read as an insult to the gods to do such a thing) - I don't know of any.