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According to this answer, we don't say tachanun on days that are yemei simcha -- days of happiness.
But the Talmud (Taanit 29a) says Mishenichnas Adar marbim b'simcha -- once Adar begins we increase happiness. Seemingly this applies at least until after Purim (14th and 15th of Adar).
But if we don't say tachanun in the entire of Nisan because we don't say it for the majority of the month (the rov), then why do we say it during Adar?
While the Talmud does indeed say that, neither the Rambam or the Shulchan Aruch mention it. Chasam Sofer (OC 160) explains why:
The statement of the Talmud (Taanit 29a) "Just as when Av begins we decrease in happiness, so too when Adar begins we increase happiness" is Rav's opinion, following his opinion that the mourning of Tisha B'Av applies to the entire month. Thus, just like by Av the mourning applies to the entire month, so too by Adar, the happiness applies to the entire month.
However, we do not hold that the mourning applies to the entire month1, and therefore there is no longer any reason to say that we should increase in happiness during the entire month of Adar.
1 See Taanit 30a.
(Credit: Double AA)
