We add a paragraph to birkat hamzon for Purim (and for Chanukka). Why is there no phrase added to the me'ein shalosh (the bracha acharona) for Purim (and Chanukka)?
This question has to do with the dispute over "ve'al hannisim" or "al hannisim."
The Mishnah Brurah (תרעב) writes that one should be careful to recite "ve'al" whereas the Shulchan Aruch quotes a minority opinion that "some sefarim have the nusach of 'al hannisim'", including the Rambam in Sefer Ahavah.
This debate was sparked by two separate sources, one in Brachot and one in Shabbos. The one in Shabbos (21b; speaking of Chanukkah) reads
".לשנה אחרת קבעום ועשאום ימים טובים בהלל והודאה"
Rashi interprets Hallel as Hallel, but Hoda'ah as Al Hannisim. This indicates that he would say "Ve'al" because he would have added it to the Hoda'ah section in Shemoneh Esreh, which is a list: "Ve'al nissecha shebechol yom imanu...Ve'al tovoteicha..." and then "...Ve'al hanissim ve'al hapurkan."
The source in Brachot reads
".ברוך ה' יום יום- בכל יום תן לו מעין ברכות"
The Gemara is speaking of putting in some short summary of the day in our Shemoneh Esreh; which appears as a separate Bracha, Ya'aleh Ve'yavo.
People like the Rambam would hold that "Al Hannisim" is the summary of the day, and would put it as a separate Bracha to fulfill Baruch Hashem Yom Yom.
Your question is one of the נפקא מינות of this debate.
Rav Lichtenstein explained: Birchat Hamazon is the lengthy version of the Bracha Me'ein Shalosh. In Birchat Hamazon, we have the Bracha of Nodeh Lcha. However, in the shortened version, there is no Nodeh Lcha-like sentence. However, on Shabbos and Yom Tov, we still add in a short summary of Ya'aleh Ve'yavo in the Bracha Me'ein Shalosh. On Chanukah and Purim we do not. The reason why is that "Al Hanisim" is a bracha of Hoda'ah, not of the Yom, and so is not placed in the Bracha Me'ein Shalosh, where there is no sentence about Hoda'ah.
Hope this helps. א פרילייכן פורים everyone!
Halachapedia has a nice write up on this:
The Maharam Rutenberg (Teshuva 70) writes that Al Hanisim is a prayer of thanks and is therefore inserted in the appropriate Berachot in Shemoneh Esrei and Birkat Hamazon. Al Hamichya does not have such a component and thus there is no mention. The Levush OC 208:12 says the same thing without mentioning the Maharam.
Mishna Berura 208:59 quoting the Gra, writes that unlike Shabbat and Yomtov where one is obligated to mention the day in Birkat Hamazon, mentioning Chanukah and Purim is only a minhag. The minhag was only adopted for Birkat Hamazon and was not adopted for Al Hamichya.
Rav Yosef Dov Soloveitchik (Igrot Hagrid Berachot 3:13 and Harerei Kedem vol. 1: pg. 302) explains that regarding Shabbat and Rosh Chodesh, the inherent kedusha of the day obligates us to mention them even in Me’ayn Shalosh. On the other hand, for Purim and Chanuka there is no inherent kedusha of the day (all types of melacha are allowed). We mention Al Hanissim simply as an expansion of the Beracha of Hodaa. Once we thank Hashem in Modim, it is fitting to mention the specific miracle of the day. The Beracha of me’ayn shalosh is a condensed version of birkat hamazon. The additions for Shabbat, Yom Tov, and Rosh Chodesh are independent portions of Birkat HaMazon and are therefore abridged and included in Me’ayn Shalosh. However, Al Hanissim is not an independent portion, and it is not the main idea of the Hodaah section.
Rav Chaim Soloveitchik (cited in Haggadah Shel Pesach MiBeit Levi pg. 233) suggests that the reason why Chanukah and Purim are not mentioned in the Me’ayn Shalosh is based on the concept of the compensatory beracha for Birkat Hamazon. The Gemara Berachot 49a-b, provides a solution for one who omits Retzei or Yaaleh Veyavo from the Birkat HaMazon of Shabbat and Yom Tov. If one realizes the mistake after completing the third beracha of Uvnei Yerushalayim, but prior to reciting Hatov Vihameitiv, one can recite a compensatory beracha at that point, and there is no need to return to the beginning of Birkat HaMazon. This beracha is only available for the additions for Shabbat, Yom Tov and Rosh Chodesh. Me’ayn Shalosh is an abridged form of all of the berachot of Birkat HaMazon. Anything that is not a beracha is not included. Although the additions for Shabbat, Yom Tov and Rosh Chodesh don't normally appear as independent berachot, they have the potential to exist as independent berachot in the form of the compensatory beracha. Therefore, the additions for Shabbat, Yom Tov and Rosh Chodesh are abridged and included in Me’ayn Shalosh. The addition for Chanukah and Purim does not have a compensatory beracha and never exists as independent beracha. Therefore, it is not mentioned in Me’ayn Shalosh. [Based on this logic, Rav Chaim explains why the additions for Shabbat, Yom Tov and Rosh Chodesh in the Me’ayn Shalosh appear after Uvnei Yerushalayim and not before. The compensatory beracha is recited after Uvnei Yerushalayim. Therefore, one should view the me’ayn Shalosh as an abridged form of Birkat HaMazon when the compensatory beracha is recited and the logical placement for these additions is after Uvnei Yerushalayim.]
See also Tzitz Eliezer 9:33 who cites a beautiful approach of the Minchat Ani. see also Rabbi Eli Mansour
see article by Rabbi Ari Enkin