“Why isn’t the new year on the 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.
https://gist.github.com/joyeusenoelle/3754e00a37fe81aa43aad3eb9543f3ce
Today you are going to learn about Mercedonius!
Lady, EVOLVED 
@noelle « By a legal fiction, the Romans treated both the first "sixth day" and the additional "sixth day" before the Kalends of March as one day. Thus a child born on either of those days in a leap year would have its first birthday on the following sixth day before the Kalends of March. When, many years later, modern consecutive day counts were laid alongside the Roman dates the sixth day before the Kalends of March fell on 24 February. However, in a leap year the sixth day fell on 25 February because the additional sixth day came before the 'normal' sixth day. » 
