There are many reasons why Nathaniel Ayers is resistant to moving into the apartment that Steve Lopez helps secure for him in a transitional housing facility for Los Angeles's homeless population. Ayers has trust issues, even with Lopez. Ayers can surely sense that Lopez genuinely cares for him, but Ayers may also be a bit suspicious of this concern, wondering if Lopez might be exploiting him to write newspaper columns about him and gain notoriety for himself.
If Ayers has trust issues with this man who he is slowly but surely building a friendship with, then he has even bigger issues with all of the new authority figures he will meet at this housing facility: doctors, nurses, managers, social workers. These are all strangers to Ayers, and he does not trust them to have his best interests in mind. A common symptom of schizophrenia is distrust of authority figures. Schizophrenics tend to be paranoid that any authority figures are trying to control them. This distrust extends to the other residents who will be Ayers' neighbors; he worries that they are all drug addicts and criminals who could steal his beloved collection of instruments. In fact, throughout the book Ayers looks down on fellow homeless people—he has a holier-than-thou attitude and tends to view them, not himself, as the truly wretched. So he is not thrilled with the prospect of living in close quarters with many other homeless residents.
Finally, and probably most sadly, Ayers has perhaps simply become accustomed to life on the streets. He has known it for so long that it is normal for him. His sensitive mental state makes him fear big changes, and moving off the streets he has called home for so long and into that apartment would be a shocking change.