You actually have two questions that need to be addressed:

1. Why do many people celebrate the 25th of December for their winter celebrations / God's birthday instead of the 21st, the actual day of the winter solstice?

Origins of solstice celebration

The seasons of the year are caused by the 23.5º tilt of the earth's axis. Because the earth is rotating like a top or gyroscope, it points in a fixed direction continuously -- towards a point in space near the North Star. But the earth is also revolving around the sun. During half of the year, the southern hemisphere is more exposed to the sun than is the northern hemisphere. During the rest of the year, the reverse is true. At noontime in the Northern Hemisphere the sun appears high in the sky during summertime and low in the sky during winter. The time of the year when the sun reaches its maximum elevation occurs on the day with the greatest number of daylight hours. This is called the summer solstice, and is typically on JUN-21 in the Northern Hempisphere -- the first day of summer. "Solstice" is derived from two Latin words: "sol" meaning sun, and "sistere," to cause to stand still. The lowest elevation occurs about DEC-21 and is the winter solstice -- the first day of winter, when the night time hours are maximum.

In pre-historic times, winter was a very difficult time for Aboriginal people in the northern latitudes. The growing season had ended and the tribe had to live off of stored food and whatever animals they could catch. The people would be troubled as the life-giving sun sank lower in the sky each noon. They feared that it would eventually disappear and leave them in permanent darkness and extreme cold. After the winter solstice, they would have reason to celebrate as they saw the sun rising and strengthening once more. Although many months of cold weather remained before spring, they took heart that the return of the warm season was inevitable. The concept of birth and or death/rebirth became associated with the winter solstice. The Aboriginal people had no elaborate instruments to detect the solstice. But they were able to notice a slight elevation of the sun's path within a few days after the solstice -- perhaps by DEC-25. Celebrations were often timed for about the 25th.
http://www.religioustolerance.org/winter_solstice.htm

2. Why do xians celebrate Jesus's birthday on the 25th of December too?

Pre-Christian origins of holiday

Christmas has its origins in several pagan holidays. The celebration known as Saturnalia included the making and giving of small presents (saturnalia et sigillaricia). This holiday was observed over a series of days beginning on December 17 (the birthday of Saturn) and ending on December 25 (the birthday of Sol Invictus, the "unconquered sun"). The combined festivals resulted in an extended winter holiday season. Business was postponed and even slaves feasted. There was drinking, gambling, and singing, and nudity was relatively common. It was the "best of days," according to the poet Catullus.[3]

During the time in which Christianity was spreading throughout the Roman Empire, another similar religion known as Mithraism was also gaining widespread acceptance. The followers of Mithraism worshipped Mithras, a god of Persian origin, who was identified with Sol Invictus. [citation needed] The followers of Mithraism, consequently, adopted the birthday of Sol Invictus as the birthday of Mithras. In 274 AD, due to the popularity of Mithraism, Emperor Aurelian designated December 25 as the festival of Sol Invictus.

Christian origins of holiday

Around 220 AD, the theologian Tertullian declared that Jesus died on March 25, 29, but was resurrected three days later. Although this is not a plausible date for the crucifixion, it does suggest that March 25, nine months before December 25th, had significance for the church even before it was used as a basis to calculate Christmas. Modern scholars favor a crucifixion date of April 3, 33, which was also the date of a partial lunar eclipse (These are Julian calendar dates. Subtract two days for a Gregorian date.).[4]

By 240 AD, a list of significant events was being assigned to March 25, partly because it was believed to be the date of the vernal equinox. These events include creation, The Fall of Adam and Eve, and, most relevantly, the Incarnation.[5] The view that the Incarnation occurred on the same date as crucifixion is consistent with a Jewish belief that prophets died at an "integral age," either an anniversary of their birth or of their conception.[6][7]

The idea that December 25 is Jesus' birthday was popularized by Sextus Julius Africanus in Chronographiai (221 AD), an early reference book for Christians. This identification did not at first inspire feasting or celebration. In 245 AD, the theologian Origen denounced the idea of celebrating the birthday of Jesus "as if he were a king pharaoh." Only sinners, not saints, celebrate their birthdays, Origen contended.

As Constantine ended the Christian persecution and began the persecution of non-Christians, Christians began to debate the nature of Christ. The Alexandrian school argued that he was the divine word made flesh (see John 1:14), while the Antioch school held that he was born human and infused with the Holy Spirit at the time of his baptism (see Mark 1:9-11). A feast celebrating Christ's birth gave the church an opportunity to promote the intermediate view that Christ was divine from the time of his incarnation.[8] Mary, a minor figure for early Christians, gained prominence as the theotokos, or god-bearer. There were Christmas celebrations in Rome as early as 336 AD. December 25 was added to the calendar as a feast day in 350 AD.[8]

http://en.wikipedia.org/wiki/Christmas

They xian's are not alone on this. Actually, any religion you study in detail becomes this absurd too.