He might actually love you and just being around people stresses him out. Schizophrenia can cause the person in question to isolate themselves intentionally because of various reasons such as being around people stresses the person out and perhaps he doesn't just come out and say it because he is afraid it will come out wrong and will hurt you or something. I'm just speaking from personal experience though, you could be right for all I know. When I was around a crap load of people I started going seemingly catatonic and couldn't handle it, for example.
My relationship is breaking apart. We never argued the whole time we were together. I love him but I don't think he loves me back even though he says he does because he never wants to see me and keeps telling me he wants space. He has schizophrenia. He says it's him - that his head is in a bad place but makes all sorts of excuses not to see me. I wish he would be truthful and if he doesn't want me then let me go..........It's 2.30 am and still no sleep - Im in a 'bad place' myself at the moment to say the least. I need to rest more than anything but it's not going to happen. Really messed up. :(
Because the bad relationship is going to cause you unduly stress and there is probably no hope of fixing it so you're better off with having none instead of a bad one.