Prior to the Mabul people lived for hundreds of years. After the Mabul lifespans shortened although we see that the Avos lived in the 180 year range. In the Pasuk in Tehilim we say Yemei Shenoseinu Shivim Shana, V'Im Bgevuros Shemonim Shana. Where does the saying "You should live till 120" come from? And why Davka 120?
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Because thats when Moshe Rabenu lived until and no one can Live longer than him two sources that discus this reason and its shortcomings:
and Wolfish Musings
I also used to think it had to do with Moshe's age. But then this made me wonder why we say "You should live till 120", since it sounds more like a curse than a blessing to limit someone's potential age to a set number of years. Then it was pointed out to me that it isn't a curse, but a determination made by HaShem, explicitly stated in the Torah.
In BeReishith (6:3) HaShem says: "לֹא-יָדוֹן רוּחִי בָאָדָם לְעֹלָם, בְּשַׁגַּם, הוּא בָשָׂר; וְהָיוּ יָמָיו, מֵאָה וְעֶשְׂרִים שָׁנָה. "
"My spirit shall not abide in man for ever, for that he also is flesh; therefore shall his days be a hundred and twenty years."
Essentially, we are saying that the person should live to the maximum age he can, which is set at 120 years as ordained by HaShem.
Rashi holds that the Pasuk is referring to something else, but I believe that is likely where the tradition stems from. Rashi's opinion is not shared by everyone.
The Torah writes about Moshe that he remained youthful and vigorous until 120 years. We thus bless each other with the designation "Until 120" with the same connotation, viz. that they should live a long life without any physical, emotional and intellectual degradation.
Although there are a number of people who lived past 120 years, only Moshe is described as living a long life without ever experiencing the ravages of old age.
It's a common mistake.
The meaning of the Pasuk you cited is that Hashem would wait 120 years before the punishing that generation (Rashi). So "till 120" hasn't came from there, if there is any source at all