Why is "Pirsumei Nissa" (publicizing the miracle of Chanukah) so important?

Question

There are 3 halachot that I have located that are related to the reason of Pirsumei Nissa - publicizing the miracle of Chanukah (Undoubtedly, there must be others:

• Chanukah candles must be lit in a window facing the public (street)
• Candles are lit in shul (See this answer)
• The haftarah for Chanukah is said even if a mistake was made in the reading of the Torah sections on Shabbat Rosh Hodesh Chanukah. (See this answer)

Why is publicizing the miracle specifically relegated to Chanukah?

By comparison, a great miracle happened on Purim, too. Why don't we publicize this miracle?

Pesach was also a great miracle. Yet reading the Hagadah is not called pirsumei nissa, and there's no mitzvah on Pesach to "publicize" it.

What's so special about Chanukah that warrants having to publicize it. And, what exactly are we "publicizing"?

Answer 1

Your hypothesis is wrong.

a great miracle happened on Purim, too. Why don't we publicize this miracle?

We do, by reading the m'gila. See e.g. https://judaism.stackexchange.com/a/64482 and Different miracle-publicization strategies on Chanuka and Purim.

there's no mitzvah on Pesach to "publicize" it.

There is: we drink four cups of wine at the seder. See e.g. http://etzion.org.il/vbm/english/pesach/pes64-bt.htm.

Answer 2

From Rabbi Bogomilsky, posted on Chabad.org:

"נר חנוכה מצוה להניחה על פתח ביתו מבחוץ" “The requirement is to place the Chanukah light by the doorway of one’s house, from the outside.” (Shabbat 21b)

QUESTION: Rashi writes that this is because of pirsumei nisa — to publicize the miracle. Why on Chanukah is pirsumei nisa emphasized as a prerequisite for proper fulfillment of the mitzvah?

ANSWER: The Syrian-Greeks endeavored to detach the Jews from Torah study. However, they did not suffice with this evil plan, but also demanded that the Jews write on the horn of the ox that they were denouncing their share in the G‑d of Israel (Midrash Rabbah, Bereishit 2:4).

They made the strange request that the Jewish people use the horn of the ox because in those days it was customary to travel on wagons and chariots which were driven by oxen. The oxen would span the roads and go from place to place, and the horn is the most prominent and visible part of the ox. Therefore, they demanded that their denial in Hashem be written on the ox’s horn so that it would receive the widest publicity possible.

To counteract this, our Sages required that when we fulfill the mitzvah of lighting the Menorah, which commemorates the miracle Hashem did because of our allegiance to Him, it is to be done so as to attract the most public attention possible.

(עי' יפה תואר על מד"ר בראשית ב:ד)

Answer 3

Interesting question. I have no source, but a possibility may be that the other miracles you mentioned (besides the correct response that we have a different way of expressing it by reading the Megillah) is as follows:

With the neis of Purim, the entire kingdom was aware of the impending crisis and the "turnaround," so the neis of Purim was well known (once we accept that Hashem was behind the scenes,so we just need to express that story and remind ourselves of the details).

On the other hand, the Chanukah miracle was clearly a miracle, but was probably known to only a handful of people so Chazal required that we each personally re-enact an actual lighting to impress upon us the miracle (which was hidden in the Bais haMikdash.)