After Summer Solstice (Longest Day) the sun's power begins to wane as the year heads towards Winter Solstice (Longest Night).
On some Pagan calendars ancient and modern, Summer Solstice is the end of the old year, the beginning of the dark half and the new year. This makes sense astronomically. Summer Solstice is on the longest day of the year. After it the days get shorter and winter approaches.
On other Pagan calendars ancient and modern, Samhain is the end of the old year and the beginning of the new year. This also makes sense. The crops continue to ripen from Summer Solstice to Samhain and at Samhain the God goes down into the underworld or the land of the dead. That resonates with ANZAC Day here in Australia and across the Tasman in New Zealand. ANZAC Day is our joint commemoration for our war dead and it is held on the 25th of April, just a few days before Samhain on the Southern Wheel of the Year.
On still other Pagan calendars ancient and modern, Beltane is the end of the old year and the beginning of the new year. This too makes sense. The Lord impregnates the Lady at Beltane and, the next day, his power begins to wane and the new year begins.
On yet other Pagan calendars ancient and modern, Winter Solstice/Yule is the end of the old year and the beginning of the new year. Again, this makes sense. The Lady gives birth to the Lord at Winter Solstice and as the Lord grows the Sun, which represents him, grows in strength.
They all make sense. The underlying meaning is the same, no matter where or when the new year is celebrated.