This week, instead of reading the regular Parshas Shemini haftarah, we read the haftarah for Parshas Hachodesh (Yechezkel 45:16-46:18).
Verse nine mentions that when leaving the Bais Hamikdosh, one should exit from the opposite gate of entry; if entered from the north, exit from the south, and vice versa.
R' Chaim Shmulevitz (Sichos Mussar: 66) brings this verse and explains, based on the Chassid Yaavetz, the problem with exiting from the same gate: Naturally, people become bored when there is no change. They feel like everything is repetitive and meaningless, so by telling people to change gates, we ensure things stay fresh and inspiring.
The Shulchan Aruch (O.C. 151:5) says the same halacha applies in a Shul; it's a mitzvah to exit from a different door from the one he entered (based on Mishnah Berura 151:21).