“Why isn’t the new year on winter solstice?”
The answer, honestly, is that the Romans had no fucking idea how to run a calendar.
Like, seriously, people notice "OCTOber" and "DECEMber" and say, "hey, those mean 'eight' and 'ten', but they're the 10th and 12th months, what's up with that?".
If you've got a little more history, you'll know that July and August are named after Julius and Augustus Caesar, and think, "oh, they added those two months and bumped the rest of the months back."
Nope. The Romans were way, way worse at calendars than that.
July and August were actually originally Quintilis and Sextilis - the fifth month and the sixth month. They were called this because the year traditionally started in March. So they had Martius, Aprilis, Maius, Junius, Quintilis, Sextilis, September, October, November, December.
Martius was named for Mars; Junius was named for Juno. We have no idea what Aprilis and Maius were named after. (No, really.) Then they got lazy and just numbered the months.
I love how much latin vocab is in the wikipedia article on Maius.
"The Romans considered May an infelicitous month. Although it began with one of the most notoriously licentious holidays of the Roman calendar, the Games of Flora (Ludi Florae), the middle of the month was devoted to propitiating the lemures, the restless shades of the dead."