What is the symbolism of jackets buttoning in the back, jackets buttoning in the front, and the bikes in The Giver?
Each of those items represent another step toward self-sufficiency, becoming increasingly more independent as one grows older.
As very young children, they are taught to help each other and to ask for help from others when it is needed by being given clothing that requires assistance - someone else has to button the jackets in the back. As children grow older, their advancing age and ability to assume more responsibility for themselves is symbolized by jackets that they can put on and button independently because the buttons are in the front. Pockets in those jackets signify the beginning recognition that they might have items to keep in their personal possession rather than depending on someone else to keep their things.
Receiving their own bike is the recognition that the child has achieved an age in which s/he is able to be trusted to go places independently, to treat the bike responsibly, to ride safely, and to accept duties that might involve needing transportation other than walking.