Why do we bless people with "ad meah v'esrim"? Aren't we supposed to believe moshiach will come by then, and there will be eternal life (according to some opinions)? Thus by giving a blessing for a finite amount of years doesn't it show the lack of belief in the coming of Moshiach?
I have a bit of a revolutionary answer to this based on a Gemoro I once learned in Erachin Daf 13b which as far as I know is the only time that the 3 word phrase of AD MEOH VE'ESRIM occurs.
The Gemoro there talks about the musical instruments the Leviim used in the time of the Beys Hamikdosh and the Mishna on the Omud Aleph says that you could not have less than 2 Chatzotzerois and 9 Kinoirois and then says UMOISIFIN ie you can add on the Gemoro on the Omusd Beys asks how many to which it answers AD MEOH VE'ESRIM up to 120 citing a Possuk in Divrei Hayomim Beys as a back-up. The phrase hit me as being unusual .Tosfos on that Gemoro printed on Daf 13a says something very interesting which to sum up it would seem that 120 was just the perfect or most Hiddur number of trumpets to have and that is what is enumerated in the Possuk and that is why it is the upper limit.
Now we all famously know that when we say Ad Meoh VeEsrim to someone it is based on the Possuk at the end of Parshas Beriishis that the amount of years a man should live should be 120 MEAOH VE ESRIM SHONOH but if you look carefully there is no word AD mentioned in the Possuk.
We find the Medrash Rabba at the end of Parshas Vayechi (Parsha 100 ois 10 )talks about very Choshuve people citing Moshe Rabbeinu,Hillel Hazokein,Rabbi Yochono Ben Zakkai and Rabbi Akiva who all lived till 120 and all of them had their lives split into 3 sets of 40.
PERHAPS (I have no source for this jump) somebody put these 3 things together a) the ultimate age a person will live to as the Possuk in Bereishis indicates is 120 (even though at the time nobody died that early-I think the first mention of someone dying earlier than that is Yoisef 110) b) the Medrash of Vayechi showing those very Choshuv people - leaders of Klal Yisroel who lived till 120 and c) more importantly the Gemoro in Erachin together with Tosfos that AD MEAH VE ESRIM is the ideal number or age and just combined them together,that you could not get a better Brocho living till 120 like those 4 great leaders and that 120 is just the most perfect number
(as the late Yeshuois Moshe -the previous Viznitzer Rebbe would say "Ich Hob GeKlert BeDerech Efsher)
Rav Shlomo Yosef Zevin of Chabad relates this story: (see Artscroll Judaica Classics: A Treasury of Chassidic Tales on the Torah, vol. I (first story Mishpatim pg. 245)
R' Tzvi of Zidachov was a student of R' Yaakov Yitzchak Horowitz, the Chozeh of Lublin (1745 - 1815).
R' Tzvi in the course of the story wished his Rebbe to live forever. The Chozeh responded that such a thing was beyond mortal man. R' Tzvi then wished his Rebbe would live until 120. The Chozeh said: "But that's not forever?"
R' Tzvi then explained his own explanation:
The Gemara in Chelek (last chapter of Sanhedrin) says that the world will last 6000 years. This is made up of a cycle of 120 "yovel" (jubilee) years.
(120 x 50 = 6000)
So when I wish you to live until "120", it means until the 120th year (yovel) which is in fact "forever" in this world, because by then Moshiach will have surely come.