Christmas is a true Holy Day, a commemoration of Christ's birth, the day God's Son became a human and began dwelling among us, an act(ion) He continues to do through His Holy Spirit.
Hanukkah, on the other hand, is a myth, a fable - or at least the "miracle" associated with it is. Unwilling and undesiring to make a popular military victory a holiday worthy of commemoration alongside the Biblical feasts and festivals, the rabbis invested the tale of the Maccabees' recapture of the Temple with a "miracle story" - in fact, several miracle stories, IIRC, the one about the flask of oil burning for eight days being the one that has survived. See, e.g., Bloch, Abraham P., The Biblical and Historical Background of the Jewish Holy Days (Ktav Publishing House, Inc., New York, 1978).
As for the true reason Hanukkah is celebrated for eight days, you can read about it in the 10th chapter of 2 Maccabees, an apocryphal intercanonical work:
1 Now Maccabeus and his followers, the Lord leading them on, recovered the temple and the city; 2 and they tore down the altars which had been built in the public square by the foreigners, and also destroyed the sacred precincts. 3 They purified the sanctuary, and made another altar of sacrifice; then, striking fire out of flint, they offered sacrifices, after a lapse of two years, and they burned incense and lighted lamps and set out the bread of the Presence. 4 And when they had done this, they fell prostrate and besought the Lord that they might never again fall into such misfortunes, but that, if they should ever sin, they might be disciplined by Him with forbearance and not be handed over to blasphemous and barbarous nations.The account in 1 Maccabees Chapter 4 (considered to be more historically accurate than 2 Maccabees, and giving no explanation for the eight days) is as follows:
5 It happened that on the same day on which the sanctuary had been profaned by the foreigners, the purification of the sanctuary took place, that is, on the twenty-fifth day of the same month, which was Kislev. 6 And they celebrated it for eight days with rejoicing, in the manner of the feast of booths, remembering how not long before, during the feast of booths, they had been wandering in the mountains and caves like wild animals. 7 Therefore bearing ivy-wreathed wands and beautiful branches and also fronds of palm, they offered hymns of thanksgiving to him who had given success to the purifying of his own holy place. 8 They decreed by public ordinance and vote that the whole nation of the Jews should observe these days every year.
36 Then said Judas [Maccabeus] and his brothers, "Behold, our enemies are crushed; let us go up to cleanse the sanctuary and dedicate it." 37 So all the army assembled and they went up to Mount Zion. 38 And they saw the sanctuary desolate, the altar profaned, and the gates burned. In the courts they saw bushes sprung up as in a thicket, or as on one of the mountains. They saw also the chambers of the priests in ruins. 39 Then they rent their clothes, and mourned with great lamentation, and sprinkled themselves with ashes. 40 They fell face down on the ground, and sounded the signal on the trumpets, and cried out to Heaven.As for "Kwanzaa," it is a total fabrication, the 1966 creation of a former Black Nationalist. I would almost consider wishing someone a "Happy Kwanzaa!" to be an insult to their intelligence, akin to wishing an adult a "Happy Great Pumpkin Day!" Yet even Halloween has more validity than Kwanzaa.
41 Then Judas detailed men to fight against those in the citadel until he had cleansed the sanctuary. 42 He chose blameless priests devoted to the law, 43 and they cleansed the sanctuary and removed the defiled stones to an unclean place.
44 They deliberated what to do about the altar of burnt offering, which had been profaned. 45 And they thought it best to tear it down, lest it bring reproach upon them, for the Gentiles had defiled it. So they tore down the altar, 46 and stored the stones in a convenient place on the temple hill until there should come a prophet to tell what to do with them. 47 Then they took unhewn stones, as the law directs, and built a new altar like the former one.
48 They also rebuilt the sanctuary and the interior of the temple, and consecrated the courts. 49 They made new holy vessels, and brought the lampstand, the altar of incense, and the table into the temple. 50 Then they burned incense on the altar and lighted the lamps on the lampstand, and these gave light in the temple.
51 They placed the bread on the table and hung up the curtains. Thus they finished all the work they had undertaken. 52 Early in the morning on the twenty-fifth day of the ninth month, which is the month of Kislev, in the one hundred and forty-eighth year [Seleucid Era; 15 December 164], 53 they rose and offered sacrifice, as the law directs, on the new altar of burnt offering which they had built. 54 At the very season and on the very day that the Gentiles had profaned it, it was dedicated with songs and harps and lutes and cymbals.
55 All the people fell on their faces and worshiped and blessed Heaven, who had prospered them. 56 So they celebrated the dedication of the altar for eight days, and offered burnt offerings with gladness; they offered a sacrifice of deliverance and praise. 57 They decorated the front of the temple with golden crowns and small shields; they restored the gates and the chambers for the priests, and furnished them with doors. 58 There was very great gladness among the people, and the reproach of the Gentiles was removed.
59 Then Judas and his brothers and all the assembly of Israel determined that every year at that season the days of dedication of the altar should be observed with gladness and joy for eight days, beginning with the twenty-fifth day of the month of Kislev.
The fact that Christmas, Hanukkah and Kwanzaa occur around the same time of the year is no reason to dilute or diminish the absolute uniqueness of Christmas by lumping it in with these other celebrations.