The Sefer HaChinuch in Parshas Bo gives a clear explanation as to why we keep a second Adar:

At the root of this precept lies the purpose that the Israelites should keep the holly days of the Eternal Lord at their proper time: For the Eternal Lord ordered Passover celebrated when the grain is in the aviv stage, newly ripened-as written, “Observe the month of' aviv (spring) and keep Passover” and the festival of Sukkoth is to be celebrated at harvest time, as it is written, “and the festival of ingathering (harvest) at the turn of the year” (Exodus 34: 22). If not for intercalation of the years, the holy days would not occur at these times.

The Jewish people reckon their months and holy days according to the days of the lunar year, which are 354 days, eight hours, 48 minutes and 40 seconds. It is less than the solar year by ten days, 2 1 hours 11 minutes and 20 seconds. The ripening of grain and produce is by the power of the sun and therefore the result is that without adding the second month of Adar, by which we make the lunar years come equal with the solar years (intercalation) Passover, would not occur in the spring, nor Sukkoth at harvest time.

This message has been edited. Last edited by: Rabbi Mitterhoff,

The Gemarah in Sanhedrin 11b says that there is a 3rd factor, which it must be time for harvesting fruits by Shvuos time. Tosfos there learns it from which the Torah calls it “Chag Hakatzer” The holiday of harvesting. See over there that if it doesn’t fit into 2 out of the 3 seasons then you make an extra month, but not if it misses only one of the seasons (there is a Shaila if you’re Maaber for Sukkos alone.) (Rashi there holds that for Pasach and Shvuos is D’rabanan, but Tosfos there argues.)

Which brings up the problem what do we do in the year 6000 when pesach will occur two months after the first day of spring?

But why Adar, specifically? According to the reasons given, we could have chosen any month to repeat.

The reason, the Gemarah in RH says, because the Megilah says that Adar is the 12th month. If you make a different month double, then Adar wouldn’t be the 12th month

I just wanted to point out the ROSH (Daf 6:- I hope) who argues with the majority and holds that the extra month is Adar only when the Rabbis declare a leap year after the month of Adar has commenced. In the event of an earler decleration, the extra month has no association with Adar. Of course now that the calender was set, according to the ROSH there would not be an extra Adar just a plain vanilla extra month.

quote:

Originally posted by Eitan Halevy:
But why Adar, specifically? According to the reasons given, we could have chosen any month to repeat.

Which other month can we say "Marbin Besimcha" by? Only in Adar and with two, it's a "Mightier Marbin Besimcha"