A few quotes from the Rabbi on 'Customs of Israel'
in which he teaches that the Tahanun prayer should not be recited when a youth, learning to put on tefillin, is present in the synagogue
The custom of Egyptian Jews is not to recite Tahanun when a youth, learning how to fulfill the commandment of tefillin, is present in the synagogue. It seems that the origin of the custom concerning a youth turning 13 years of age lies in the fact that at this moment he resembles a groom, as the Magen Avot wrote, in section 225, in the following words: "It is a mitzvah for a person to hold a festive meal on the day his son becomes Bar Mitzvah, just as when he comes under the wedding canopy." End quote. His joy engages the congregation, so that they do not recite the Tahanun. The congregation is also joyful because an additional adult has joined them. Also, it was the custom to put tefillin on the youth on the exact day of his Bar Mitzvah, and some may have thought that laying Tefillin precludes reading Tahanun, so that even in our day - when the precise age of the youth is not taken into account, and some put on the Tefillin before [the date] and some do so after (which is not according to rule) - the custom, not to recite Tahanun on the day of the laying of Tefillin, has remained.
Shnot Haim im Mekor Haim, section 8, halakhot on Tahanun, paragraph 10 p. 29b, Halevy Zuckerman Printing, Jerusalem, 1921