Q: When the 10th of Teveth falls on Friday, why are we allowed to fast on Friday and not bump it back or forward as other fast days?

A. The fast of Asara b’Teves occurs on a Friday about 20 % of the time. (next one will be Dec. 13, 2013). The fast continues until after the completion of Maariv for Shabbos.

The Avudraham (Taanios p. 254), in the name of the Responsa of the Geonim, mentions that unlike other fast days (except Yom Kippur) if the Tenth of Teves were to fall out on a Shabbos this fast would actually be observed on that day. This is because of the verse “Etzem Hayom Haze” (“this very day”) mentioned in Yehchezkel 24-2, is similar to the phrase “B’etzem Hayom Haze” written in regards to Yom Kippur in Vaikrah 23-28.

He further explains that our calendar calculation is such that the only public fast which can fall on Erev Shabbos is the tenth of Tevet. He adds that if the 13 of Adar falls on Shabbos, we move Taanit Esther back to Thursday, to avoid not being able to proper prepare for Shabbos.

Kol Bo mentions another reason, that it is Darkei Haemori, as other religions fast on Friday. Evidently this is not enough to override the Etzem Hayom Haze.

See also Chidushei R. Chaim (Stencils – Rosh Hashana), who explains that Asara b’Teves is similar to a Taanit Chalom, the fasting for a nightmarish dream, that one observes even on Shabbos, since it brings relief only when kept immediately. Some further explain that Asara b’Teves is not essentially only a historical fast day of mourning, but rather, like Taanit Chalom, a day of fasting for an actual occurrence of today, as it is in this day that the Heavenly Court decides if the Geulah will take place in this particular year. (Chasam Sofer Vaikra- Drush Zain Adar, see also Ohr Sameach H’ Taanis 5-6).

Rabbi A. Bartfeld, as revised by Horav Shlomo Miller Shlit”a