Kylo Ren is fixated on eliminating anything that has to do with his past, which is exactly why he could never be as powerful as Darth Vader.
More of what makes the powerful and troubled Kylo Ren tick is explored in Star Wars: Legacy of Vader #1. Written by Charles Soule, pencilling by Luke Ross, and cover art by Derrick Chew.
Star Wars: Legacy of Vader traces Kylo Ren's journey as he becomes Supreme Leader of the First Order and tries to reconnect with the ghost of his grandfather, Darth Vader.