If Rosh Chodesh is a "Zeman Kapara" (time of atonement) as we say in the Mussaf prayers, why does it contain no selichot and no tachanunim? Why doesn't it (the day of Rosh Chodesh itself) resemble Yom Kippur in that way, which is full of selichot?
The kapparah of Rosh Chodesh is different than the regular type.
On one level, the goat offered as a chatas on this day (also on the other Yamim Tovim, incidentally, except for Yom Kippur) is to atone for cases of tum'ah involving the Beis Hamikdash or sacred foods where there was "no knowledge at the beginning or the end" - in other words, the person never knew that he was tamei before he entered the Beis Hamikdash or ate the food, and never found out afterwards either. (Shevuos 2a)
So perhaps this makes it inappropriate for us to substitute for this tachanun or selichos, in which we regret the sins that we do know of (which we may have done deliberately or inadvertently) and ask Hashem to forgive us for them.
On a deeper level, too, there is the idea that the kapparah is not for us but, so to speak, for Hashem's having diminished the moon's size* (Chullin 60b). Again, then, this wouldn't fit with us mentioning our own misdeeds.
(What about the phrase לכל תולדותם, apparently implying that the kapparah is "for all generations" of Jews? Kuzari (3:5), cited in Beis Yosef (Orach Chaim 423), states that indeed תולדותם means "the rebirths of the months" - i.e., that Rosh Chodesh is a time of atonement for the entire month, and perhaps also this includes the idea that it is an atonement for the very fact that the moon needs to reborn each month.)
* What does this mean? A lot of different explanations have been given, but here's one, from Chabad.org. Key paragraphs: