They insist Jesus could not have been observing a Holy Day never actually ordained in The Hebrew Bible. That Daniel foretells the history that produced Hanukkah isn't enough for them.
They insist this "dedication" refers either to the second of Adar when the Second Temple was first dedicated. Or to how Solomon originally Dedicated the Temple with an expansion of Tabernacles to 14 days, and feel that's backed up by this following John 7-9.
The latter requires expanding the definition of Winter, (maybe so does the former, but sometimes Adar can fall during a pretty cold period). But the point is it doesn't say the anniversary of the dedication, it said the Feast of Dedication was being observed. The 25th of Kislev is the only Feast the Jews ever celebrated by that name.
Also I firmly believe the Expansion of the Festival Solomon did was the prior week not the following Week, since it clearly defines the 22nd as the day the Festival ended, and the 23rd as they day everyone went home. The only objection offered to it being the prior week is the assumption of Yom Kippr being a Fast Day. The Bible never links the word Fast to Yom Kippur, in fact God expressed disapproval of annual Fast Days in Zachariah. The basis for making Yom Kippur a fast day is that the people were to "afflict your souls", fasting is a way to do that but not the only way (Jesus was afflicting His soul without fasting in Gethsemane). Either way it would be merely the 2nd or 3rd day of a two week festival being toned down by people doing whatever they feel is best to keep that command. Besides with what is supposed to go on in The Temple that day I could easily see it being treated as part of the Festival.
Also 2 Chronicles 7:9 says "And in the eighth day they made a solemn assembly: for they kept the dedication of the altar seven days, and the feast seven days." Which clearly defines the extra 7 days as coming first.
As far as the lack of Old Testament precedent they complain about, leaving Daniel aside for a moment.
Haggai 2:10-23 is a revelation God gave to Haggai on the 24th of Kislev, and it foretells that very day being a time to rededicate the Temple. Reading 1 Maccabees chapter 4 (it's at the end pretty much) it would seem the 24th was the day they were actually done rebuilding and cleansing everything, the 25th was the day the new Sacrifices were made.
The whole "Menorah burning for 8 days on 1 day's worth of oil" is a made up fairy tale from much later tradition. 2 Maccabees 10:1-8 tells us it was an 8 day festival because it was done in the manner of the Feast of Tabernacles. Some have conjectured the original logic was a counterpart for Tabernacles of the Second Passover law from Numbers 9. One reason to make it two months later rather then one would be the Eight Month's affiliation with The Feast of Jeroboam. But if that was the only factor it'd have been on the 15th not the 25th. Haggai's prophecy I'm convinced is why this was when it was whether they knew it or not. Actually the text of Haggai in question discuses the same issues that make Second Passover necessary in Numbers 9, and since Haggai's previous vision was during Tabernacles, it seems valid to interpret him as validating a Second Tabernacles Law.
The Hebrew word Hanukkah (Dedication) first appears in The Bible in Number 7:84&88 ("Dedicating" was used twice much earlier in the same chapter) this Chapter is about the original Dedication of the Tabernacle and may be one likely drawn on at the first Hanukkah. That right after this Aaron is instructed to light The Menorah could be the original reason The Menorah became important to Hanukkah.
Also if you do the math in Genesis, the 26th or 27th of Kislev is when the 40 days of rain that caused the Flood stopped. And it's been popular to see the Nine Candle Menorah of Hanukkah foreshadowed by Zechariah 4.
Back to Daniel, some people, especially those who want to late date Daniel but knowing they can't make it too late due to DSS manuscripts. Will insist it discuses Antiochus Epiphanes and his persecution, but not the Maccabees actual victory.
Daniel 11:32 "And such as do wickedly against the covenant shall he corrupt by flatteries: but the people that do know their God shall be strong, and do exploits." One Bible I have in it's marginal footnotes suggests "Take Action" as an alternate translation of "do exploits".
But more directly relevant to the idea of The Re-dedication being Biblical is Daniel 8:13-14.
"Then I heard one saint speaking, and another saint said unto that certain saint which spake, How long shall be the vision concerning the daily sacrifice, and the transgression of desolation, to give both the sanctuary and the host to be trodden under foot? And he said unto me, Unto two thousand and three hundred mornings and evenings; then shall the sanctuary be cleansed."The Number 2300 mornings and evenings (1150 days) is the main reason this verse in it's details I feel applies more to Antiochus then The Antichrist, I like Chris White's explanation of it, It does fit to say the time from Antiochus' Abomination first being set up until the Maccabees rededicated The Temple. But it's pretty hard to make it line up perfectly with Revelation where it's always 1260 days or 42 months being mentioned.
The point is, that the Cleansing of The Temple in 164 BC was part of Bible Prophecy.
Josephus talks about the origin of Hanukkah in Antiquities of The Jews, Book 12, Chapter 7 in section 6 and 7, the last part of the chapter. He there directly links it to Daniel's Prophecy, which I will admit the Books of Maccabees fail to do.
An argument might also be made that John 10 doesn't tell us Jesus was celebrating or observing Hanukkah, He just happened to be there at that time.
During His ministry I find it interesting that Jesus was in Jerusalem only on Holy Days, with John in particular linking Holy Days to anytime He was even in Judea. In fact in the entire Gospel account of his life the only time we are told He was in Jerusalem when it wasn't specifically a Holy Day was to fulfill the Torah's law about being presented in The Temple 40 days after His Birth.
I'm convinced every detail of Scripture is there for a reason, and The Holy Spirit wanted us to take note of the fact that Jesus was in Jerusalem during Hanukkah.
I rant more against anti-Hanukkah Christians here.
Update 1/11/2016: I've found a site online called "Why Yahshuah Refused to Celebrate Hanukkah".
First of all "Yahshuah" is an interpretation of how to properly render Yeshua affiliated with a peculiar brand of the Sacred Name movement. So be warned.
First this site claims John 7 is about Hanukkah, (it talks about the connection between Tabernacles and Hanukkah that I talk about above), then says the John 10 reference is just continuing the same narrative. However an unqualified reference to Tabernacles always means the Tishri celebration just as an unqualified reference to a Feast of Dedication means the Kislev one. And John 10:22-23 stylistically is clearly the start of a new incident that clearly dates itself to a different time then what came just before.
This site actually claims The Jews of this period stopped observing Tishri Tabernacles all together and just replaced it with Hanukkah. There is no evidence of that, 2 Maccabees 10:6-7 says it was observed in the manner of Tabernacles but in no way says it replaced that feast.
Josephus has I'm pretty sure clear references to Tabernacles still being observed in Tishri at this time. When Josephus describes the origin of Hanukkah which I mentioned above he doesn't mention the link to Tabernacles that only 2 Maccabees directly makes (Josephus seemed to only know 1 Maccabees) and only called it the Festival of Lights. So it's highly unlikely Josephus ever meant that any time he refereed to Tabernacles.
After making that argument they make a thing out of Jesus refusing to go up to the Feast when it started. Then says when He did show up He condemned them for not following The Law.
Read John 7 more carefully, He did go up at the same time his brothers did more or less, but was simply in secret till the midst of the Feast. And what Jesus talks about at this time the site misrepresents completely. He was observing that Feast as much as He was Passover during the Passion Week, where he also argued with the Pharisees and Sadducees.