He made the boxes because he was lonely. He didn't have anyone to love, and he made the boxes so he could love them, and so people would know that he existed, and because birds are free and the boxes are hiding places for the birds so they will feel safe, and he wanted to be free and be safe. The boxes are for him so he can be a bird.
The Time Traveler's Wife (ed. Simon and Schuster, 2014) - ISBN: 9781476764832