Ok so in the Bioshock trilogy there are parallel universes all connected. In infinite it's a parallel universe to the one Booker lives in and Elizabeth is Bookers daughter who he gave up to relieve him of his debt. Well in this parallel universe where Columbia is, Comstock is a version of Booker that accepted baptism so he became a religious tyrant thus going on to lead Columbia. So Elizabeth sees that the only way to ensure Comstock never comes to power and rules is to kill the versions of Booker in each parallel universe so that there may never be a Comstock. Hence why at the end she kills you.