Hi utter nutter,
Services suck...and I had the same experience as you for years. Unfortunately, some CMHTs only deal with "severe and enduring mental illness" which in their limited vocabulary only include schizophrenia/bipolar and other psychotic disorders - or possibly severe, enduring depression.
Self-harm doesn't always indicate a mental illness, but they are still wrong that there is "nothing wrong with you" - because noone should feel so bad that they have to hurt themselves. It just means that you don't fit into their li'l tick boxes, and so it's easier for them to not accept you as a patient.
It sounds like, from what you've said, that you're still in the "assessment process" - and as such you won't be on the CPA yet. You get put on that once you're receiving treatment from secondary MH services - and even then, in most cases, it's mainly a "paper exercise" with no real benefits to it anyway!
I've been seeing my T and psych (it's not strictly secondary MH services where I go - but a specialist SH team) for 2 years, and have had 1 CPA meeting. It tends to be more useful if you see lots of different people (social worker/occupational therapist/psychologist etc) because it makes clear about who's supposed to be doing what etc...but as I just see 2 people, it was just 3 of us in the room saying "yeah, things are going well...see you in 6 months" (even though I was still seeing them weekly for stuff anyway!)
I'm sorry they're being rubbish with you. Unfortunately, it's not an uncommon experience