Booker DeWitt was stuck in a never-ending loop. It didn't matter what he did Elizabeth(Anna, his precious Anna) would always be taken by Comstock. All because of the failure he was as a person. If he found religion he became a fanatic Comstock and if he stayed Booker he lost Anna. The cycle was never broken. In a thousand different worlds Booker and Comstock danced this macabre charade and because of this Anna-no Elizabeth would be the one hurt. Everything he touched broke. His wife and his daughter it didn't matter cause he broke them to. It was why when they reached the baptism and Elizabeth told him what it would take to make sure Comstock couldn't exist he willing allowed his daughters to drown him. Seeing all those Anna's/Elizabeth's he'd screwed up told him he was doing the right thing. But what Booker Dewitt never realized was there would be a version of himself that would not let Elizabeth drown him. Comstock was Booker and Booker was Comstock and it would always be so. They were completely interchangeable. They were the different sides to the same coin. Comstock knew this and so he stole a Booker's conscience and his own from a different world to create songbird. Songbird would be the perfect protector/capture. He was protective like Booker and determined to keep Elizabeth in her cage like Comstock.