Is Christmas really the birthday of Jesus?

We can say with all probability that the 25th December is not a real birthday
of Christ. This day was celebrated as a Christian feast first in the middle of
the 4th century. There are many theories about the reasons of the choice of the
25th December since the Bible does not provide any clear information in this
matter.

(a) historical theory of religion
The 25th December has some connection with feasts of other religions. The
Christians borrowed a feast from some neighbouring religion or they deliberately
wanted to supersede such one. In fact, the cult of Sun was in the beginning of
fourth century popular in the Roman empire and it has been suggested that the
25th December was celebrated as a birthday of Sun. In any case the time round
about the winter solstice was psychologically favourable for all sorts of
celebrations.
The length of the day begins to grow, the light wins over the
darkness. Why not now also remember the birth of Christ, the real sun of
righteous? The pre-Christian Germanic tribes had their Yule (or Midwinter)
feast in this season of the year, too. Especially in the nineteenth century and Nazi times
many believed that the Christians had borrowed the Yule feast and used it for their
own purposes.

(b)computational theories
There are several such theories. For example, the following alternative. The
ancient Christians commonly believed that all in Christ must be complete. So they thought that the Lord had been born and died on the same day of the year. In the year 29, the
Jewish Easter (which could be thought as being Jesus' day of death) was 25th
March. Obviously, the day of death could not be celebrated joyfully like the birthday
but they concluded that Christ was instead conceived that day and so would have
been born nine months later, 25th December. In the year 30, (an alternative
possible Jesus' day of death) the Jewish Easter was 6th April. Before the
spreading of the 25th December, the birthday of Jesus was remembered,
especially in the eastern parts of Christianity, on 6th January, nine months
after the 6th April.

c)Old Testament prophetic theory
The Jews celebrated their hanukka /chanukka feast on 25th of month Kislev (which
falls on November or December). This feast is a joyful remembering of the
rededication of the Jerusalem temple. The Christians read the prophecies of
Haggai (2:18) and Zechariah (4:6-10) as hints to Jesus Christ. In the New
Testament Christ was called many times "the head of the corner" (Math 21.42) and
connected with the temple (John 2:19 ; Matthew 26:61). The remembering of
Christ's birth on 25th day of the month can have Jewish roots like other great Christian
feasts Easter and Pentecost. The dates are almost the same but the meanings have
changed.

Main source:

Becker-Huberti, Manfred
Feiern-Feste-Jahreszeiten. – Herder, 1998.