The feasts or festivals of Christmas and Hanukkah are usually associated in the U.S.A., so that children in both religions can receive gifts, etc., etc. S, this is a good occasion to say to all of you, Merry Christmas and/or Hanukkah.
Personally I find the association of the two festivals odd or simply incidental. My view is that a different association should obtain, such as Hanukkah and Holy Thursday in the Easter season, as I will explain for those who are not too familiar with their historical backgrounds.
Hannukah is also called the Festival of lights or, to be sure, of the oil lamps, which involves the use of a candelabrum, a candle-holder for eight candles. The original candelabrum (like the one taken by Titus from the Temple in Jerusalem) had sockets for seven candles. In more ancient times, there must have been a "lampadarium" or lamp-stand for seven lamps. According to a legend, when the Temple was re-dedicated to God [Yahweh] after Antiochus IV who had dedicated the temple to Zeus, seven lamps were lit, and even though there was not much oil, the lamps remained lit overnight. (I understand that the word "hanukkah" means or refers to the "dedication" in question.)
Why SEVEN lamps, to begin with? Here is my theory: Each lamp represents a natural luminary, namely a bright and observable light, which the ancient Greeks [Iones] of the Levant [supposedly the offsprings of Iaphet]and observed and later called Planets. While shifting from the pagan to the Hebrew religion, the Israelites kept their Greek tradition and saw the sun and he other so-called planets as creatures of God. In effect, the seven luminaries belong to a Greek-Hebrew cultural tradition, which is not literally stated in the books of Genesis. Thus Hanukkah is the festival of creation and is central in the religion and theology.
The Christians (who adopted the Bible), do not celebrate Hanukkah or the rededication of the Temple, but at least in the Catholic tradition (which I am familiar with), on Holy Thursday before Easter, there is the full reading, in church, of the Genesis accounts (which I heard before I ever read them). On Easter sunday, there is the lighting of the Paschual candle), which is reminiscent of the evening lighting of the lamps in the Temple.
Both religions go back to the ancient festival of the Sun (or Apollo the sun-god) on the first Sunday of any month, while the other days of the week were reserved for the other Planets and are evident in the names of the days of the week: Lunae Dies [Dayof the Moon; Lunedi` in Italian] Martis Dies, etc. In the old Jewish calendar, Sunday was called Sabbath, which was the day of rest in creation and was a religious holiday. (English preserves the name "Sunday", whereas Italian, for instance, follows the Catholic liturgical "Day of the Lord": Domenica. The Italian 'Sabato" replaced the Latin Dies Saturnii: Saturday in English.)
Anukkah historically belongs to the Easter season, but since it is celebrated in connection with Christmas, two joyful events are celebrated by creationists and Christians respectively. The seven ays of creation in the Bible are modelled after the seven days of the week, which used to be dedicated to the seven planetary gods in the Greek world 9culture).