As you are all aware the calendar we follow the calendar that is called the Gregorian. The earth year normally has 365 days. The sun crosses twice the equator one in autumn &other in spring .The phenomenon is called equinox. Namely the autumn & spring (vernal).the one occurs in September& the other in march. Between these two time periods the sun crosses the cancer &Capricorn tropics(kataka & makara).This occurs somewhere in end June &december. According to hindu calender makar sankarnti is observed on 14th of january.According to some Christians having older belief living in parts of israel jesus was born on 6th of january &7th day hence i.e; on 12night/13th morning they might have celebrated new year .unlike the current 25th december&7th day hence that is 1st of january .what ever may be the mathematics of it may be 21st/22nd of december/1stof january/14th january it is precise that the sun starts moving north on its axis & that needs celebration. To quote gita here:

agnir jyotir iha:shukla:shanmawsa uttarawyanam.

tatra prayawtaw gatchanti brahma brahma vidhow janaw.

dhoomow rawtris tathaw krishna:shanmawsaw dakshinawyanam.

tatra chandramasam jyotir yogee prapya nivartathea.

Those who realised the brahman depart their body under fiery of the sun /in the auspicious moment of bright day light.The moon shall be waxing i.e;shukla paksha ,or during sun travel towards north.They attain the supreme reality.

A yogi who passes away in darkness& in krishna paksha or when travels south comes back to this world after reaching moon.

hari ooom tat sat.