The Gemara in Megillah 31a says that on the last day of Sukkos the Torah reading is the parshah of Vezos Haberachah and the maftir is Vaya’amod Shlomo (Melachim 1:8). The Rishonim are bothered by the following question: the Mishnah in Megillah says that Moshe Rabbeinu instituted what portion of the Torah should be read on each of the Yamim Tovim. Each portion relates to that particular Yom Tov. What then is the connection between Vezos Haberachah and the last day of Sukkos?
One cannot answer that it is because we are scheduled to read that parshah in our weekly reading of the Torah, because on Yom Tov we never continue from that reading. Also, the Mishnah states that the reading for each Yom Tov was instituted by Moshe Rabbeinu and must relate to that Yom Tov.
The Ran, on the page of the Rif (Megillah 11a), says that it is because this is the last of the Yamim Tovim and therefore we finish the Torah cycle on that day.
The Sefer Hamanhig writes in the section of Simchas Torah that on the last day of Sukkos we read the parshah of Vezos Haberachah because Shlomo Hamelech would bless Bnei Yisrael on the eighth day of Sukkos. Therefore we read Vezos Haberachah on that day, which is the parshah in which Moshe Rabbeinu blessed all of Bnei Yisrael as well.
The Gemara in Sukkah 48a says that Shemini Atzeres is a separate Yom Tov from Sukkos regarding six things. One of them is berachah. Rashi quotes a Tosefta that explains that berachah refers to the blessing of the king, for as it says: “On the eighth day he [Shlomo Hamelech] sent the people off and they blessed the king.” Earlier in that perek the Navi tells us that Shlomo Hamelech blessed the nation on that day before the nation would bless the king.
The sefer, Harirai Kedem, explains that the Gemara in Zevachim 102a says that Moshe Rabbeinu had the status of a king. Similarly Rashi in Shavuos 15a (d”h vechain ta’asu) also says that Moshe Rabbeinu was a king. The Even Ezra and the Ramban, on the pasuk in Vezos Haberachah, “vayehi vishurun melech…” explain that the melech in the pasuk is referring to Moshe Rabbeinu.
Now we can understand the answer of the Sefer Hamanhig. Since Shemini Atzeres is a separate Yom Tov regarding the fact that the king would bless the nation, we read the parshah in the Torah that discusses the blessing of the king – namely Moshe Rabbeinu, who was a melech.
The fact that the haftarah that we read on Shemini Atzeres is the parshah whereby Shlomo Hamelech blesses the nation and the nation blesses him is testament that the reason why we read Vezos Haberachah is because it discusses Moshe Rabbeinu’s blessing of Bnei Yisrael. And as we know, the haftarah always follows the general theme of the Torah portion that was read.
It was the custom of many people in Lita and Russia to go to the rav’s house after davening to bless him and to receive his blessing. The source for this custom is that our rabbanim are considered to be kings, as Chazal tell us: “man malki rabbanan.”
There is one other point that I would like to mention regarding the reading of Vezos Haberachah. When the chassan Torah is called up, the gabbai says, “amod, amod, amod….” Why is amod said three times?
The Gemara in Berachos 34a says that when someone is asked to daven for the amud he should refuse the first request, then act unsure on the second request, and finally accept the third time he is asked. However, regarding an aliyah to the Torah, the Gemara in Berachos 55a says that if one is called to the Torah and refuses the aliyah, his life is shortened. The difference between the two is simple. Davening for the amud is an honor, whereby it is not proper to ascend immediately without first refusing. Receiving an aliyah, on the other hand, is a mitzvah – and one may not refuse to perform it.
Based on this the sefer, Harirai Kedem, suggests that the aliyah of chassan Torah has both of these components: it is an honor and it is an aliyah to the Torah that cannot be refused. Therefore we call up the oleh three times so that he is not put in the position of having to refuse the first two times (since we’ve already called him up three times). At the same time it is not improper for him to ascend immediately since he was already called three times.