A source cited in the Talmud states “A child … who can take care of tefillin, his father acquires tefillin for him.” (Tosefta Chagiga 1, Succah 42a) Parents acquire tefillin when a child becomes old enough that he can care for himself and his tefillin. One can give this whole discussion a symbolic explanation.
These concepts that we have been discussing parents teach to their children from a very young age. Parents invest a lot of effort over the course of many years to teach these concepts to their children. The father ties these central concepts that are in the tefillin onto the child’s body when he is old enough to care for himself and his things. Through this the child internalizes these subjects until they actually become part of him.
Every Bar Mitzvah boy knows the importance of the Unity of the Creator, Divine Providence, reward and punishment, the exodus from Egypt and the rejection of Avoda Zara.