Why Don't we Say Tachanun on a Particular Day?

Question

There are many days on which we don't say Tachanun, and much argument about whether we say it on any given day -- but is there any underlying reason why we wouldn't say it, a reason which might explain why we do or don't say it on a given day?

I looked in the Rambam and the M"B and all I saw was lists of when we do and don't say it -- no reasoning behind why. There were some explorations of why a specific day might be excluded, but no generalizable rule through which I could then predict whether on another day we would say Tachanun.

Is there a rule which determines saying or not saying Tachanun, or is the entire practice a series of individual cases with separate logic for each?

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_{A similar question, but about Tu Bishvat specifically.}

Answer 1

R Reuven Slater wrote a very interesting book on the background and explanation of Tachanun. He answers your question as such

• Generally speaking we not recite Tachanun on days that reflect festivity
• We don't say Tachanun on Tisha b'Av as it will one day be a day of great joy marking the arrival of the Messianic area - others say because we are like aveilim on Tisha B’Av (see below) or because it is called a Yom Tov (see here, p. 16)
• We don't say Tachanun in the presence of a hatan or baal ha'brit (father, sandak, mohel) because of their joy
• We don't recite Tachanun on minha from day before, the same way an avel (mourner) interrupts his aveilut on Friday afternoon daytime (thus showing the time of simcha begins before nightfall) - Tachanun shares some features of aveilus because of its serious and somber nature
• Tachanun is not recited in a house of mourning, because aveilut represents darkness, a time for strict judgement. Reciting Tachanun highlights our faults which may in turn cause Hashem to deal with us more harshly. Others say that aveilut is comparable to Yom Tov (see here, p. 3, note 2)

On whether or not to skip Tachanun on yahrzeits, in the introduction of the book, R Yisroel Reisman brings the Minchas Elazar (the Chassidic leader of pre-war Munkatz)

Regarding Tachanun - the custom of people, who call themselves chassidim, is to be lenient. This is without merit and deserves ridicule. Their contention that [tachanun be skipped] due to a yahrzeit is laughable and causes pain to the heart. There is no day which is not the yahrzeit of thousands, perhaps tens of thousands of great, righteous men... (Divrei Torah 3:83)

I think this covers all cases mentioned above in the comments.

For further references see also Halachically Speaking vol. 9 issue 12