Question: Why is tachanun not recited in a beis ovel?
Answer: The Shulchan Aruch (Orach Chayim Siman 131 Se’if 4) quotes this minhag of not reciting tachanun in a beis ovel. The Mishna Berura (s.k. 20) writes that this minhag applies for the duration of shiva.
The Taz maintains that other people who are davening together with the ovel also do not recite tachanun, even after they leave the beis ovel. (The Mishna Berura (ibid) quotes differing views regarding the other attendees of the minyan reciting v’hu rachum on Monday and Thursday – after leaving the beis ovel.)
The Mishna Berura (ibid) explains that since the ovel is currently subject to din, it is inauspicious to recite tachanun, “which can increase din”.
Mishna Berura (ibid) adds that this applies to the beis ovel specifically, but if the ovel is davening in Shul, the other mispalelim should recite tachanun, and only the ovel should not recite tachanun.