Kaneki moved out when he turned 18 to get away from his abusive relatives who didn't really like him or want anything to do with him. After his mom died, her life insurance was left as a trust for him, which is where his living expenses came from. Upon graduating from high school, he was able to get the entire thing and moved out to live by himself.
His "family" didn't give a damn about him, and as we find out, aside from Hide, he had no close friends, since he was emotionally distant and withdrawn. Instead, he preferred to read in quiet places by himself, aside from the occasional friends by association with Hide.
However, in the manga, there were missing person flyers posted around after his sudden disappearance1 following his kidnapping by Aogiri. Even Touka didn't know where he was most of the time after that, because he distanced himself from them to protect them, while Hide was actually covering for him, saying he just had some family troubles and wasn't feeling well and just wanted some time alone. The coincidence between the disappearance of Kaneki and the appearance of Eyepatch became an important clue for the CCG to discover Kaneki's identity as Eyepatch. Although Hide had been covering up for Kaneki, once they had made the connection, Hide basically told them everything to try and get them to agree to help him, which was why he was trying to tell Kaneki to give it his all to try and impress the CCG enough to consider him worth keeping around.
1 Kaneki continued going to college all the way up until that point in the manga.