http://revach.net/article.php?id=2263

Section: Moadim   Category: Lag BaOmer
Why Meiron For an Upsherin-Chalaka? A Hint From Rav Nachman MiBreslov
The Arizal was known to bring his son to Meiron on Lag BaOmer for a haircut (Tshuvos V’Hanhagos 2:246).  What is the connection between Rebbi Shimon Bar Yochai and haircuts?  

Rav Nachman MiBreslov quotes the Gemara in Shabbos (138b).  The Chachomim in Yavneh predicted glumly that in the end of the days Torah will be forgotten from Klal Yisroel. Rebbi Shimon Bar Yochai boldly refuted this by referring to the pasuk in VaYeilech (Devorim 31:21) “Ki Loi SiShokach MiPi Zaroi”, literally meaning “it will not be forgotten from the mouth of the children.”  Rav Nachman points out that the last letters of these words spell “Yochai” the father of Rebbi Shimon.  The hidden meaning says Rav Nachman, is that since Rebbi Shimon wrote the Zohar and the Zohar explicitly says that learning the Zohar will take us out of Galus and bring Moshiach.  Therefore the pasuk mean that the Torah will not be forgotten “because of the child” of Yochai who wrote the Zohar.

Rav Yosef Berger in his Gilyon Peninim U’Parpera’os suggests that since the three old haircut is a child’s rite of passage into Chinuch, we therefore bring the children to Meiron for this ceremony to show how true Rebbi Shimon’s words still remain after a bitter two thousand year galus.  The children are on their way to be indoctrinated into Torah and Mitzvos.  The children have truly not forgotten.