That's a common misconception. For the Romans, the year used to start with March and only have ten months. January and February weren't even named, it was just the time between harvest and the new year. Several calendar changes followed over the centuries. Adding two months (January and February). Moving the new year to January, which made September-December no longer 7-10. Adding random one-off months to realign with the seasons. And a couple different tries at leap days, among other things.

This gives a quick overview.

Edit 2: To clarify, the above changes were all made by the Romans, they only started with a ten month calendar.

Edit: The fifth and sixth months were originally named Quintilis and Sextilis before they were changed to July and August.

Tbf, the calendar before them was even worse

I suppose we could fix it by moving the start of the year to March 1st. Start of spring makes more sense for the new year anyway.