While the secular New Year falls in the middle of winter (well, in the Northern Hemisphere anyway), when the earth resets itself, the Jewish New Year comes in the fall, just before the traditional harvest time. People come home from summer vacations, school starts up again, and wham! We're hit with the Ten Days of Repentance. Perfect timing, I think.
Now is the time, as we are preparing for what most of us think of as "the year," that we need introspective moments. Vacation is over, and it's back to the grindstone; what better time to take stock, to engage in heshbon ha-nefesh (accounting of the soul), to examine our relationships. The next big vacation is ten months from now, and from this point to that will be a blur of activity. Better to enter it with some deep, probing consideration.
January 1 may be a new year of the Earth, but Rosh Hashanah is more a New Year of the soul.