Q. Thank you for your answer (2699) explaining well why do Cohanim turn their back to the Aron Hakodesh. The fact is, that it is not only the Cohanim who behave so, in most shuls and yeshivot, the rabbis when they address the congregants, also turn their back to the Holy Aron containing the Sifrei Torah. Why?
A. Rambam (H. Tefilah 11: 4) describes how the people should sit in our botei knesios, “The elders sit with their faces towards the people and their backs to the Heichal (the Aron Hakodesh).” Kesef Mishne (ad loc) explains that this is permitted in honor of the attendants. Since they pay their respect to the elders, placing them up front, the elders should reciprocate and honor them by facing them.
His source is a Tosefta (Megillah 3: 14) that portrays Moshe Rabbenu teaching to the people “as he stood at the entry of the Ohel Moed” (Vayikra 8), facing them with his back towards the sanctuary. We therefore deduce, that the honor of the people here, preempts the homage of the Heichal.
Lebushei Yom Tov (O.H. 7) adds that if just seating with their backs to the Heichal the Rambam permits for the elders, certainly one teaching the Torah of Hashem and thus honoring Him, is allowed to face the people. One may add, as mentioned in question 2699 in regard to the blessing of the Cohanim, that teaching properly the Torah of Hashem to the many, is tantamount to representing the Shechina itself.
Minchas Yitzchok (5: 78) adds another practical reason. Since it is imperative that the ones listening to Torah being taught, should face their teacher (Eiruvin 13), if the Rabbi would be in the back or at the bima facing the Aron Hakodesh, they themselves would now have to turn their back to it; better one than many.
Taz (Y.D. 282: 1) maintains that the reason Rabbis teach with their back towards the closed Aron Hakodesh, is that the Sifrei Torah therein are considered being in a separate reshus or domain, and thus permitted.
Rabbi A. Bartfeld as advised by Horav Shlomo Miller Shlit’a