Speaking as someone with a fair bit of understanding of both sides of this issue, i'm actually inclined to agree with your therapist not wanting to address a diagnosis. I see two major potential reasons why your therapist hasn't discussed a diagnosis with you.
The first is that often, diagnoses can actually be counterproductive towards therapy. Yes, it helps provide a piece of the puzzle for who you are, but ultimately, it's a name ascribed to a specific set of symptoms. It's a box to put you in. And very often, people can fixate on that box, and start to see themselves as "an [x diagnosis] person", rather than a person
who happens to have [x diagnosis]. In traditional medicine, you can assign a diagnosis to a person, and it tells you everything you need to know about what's making them sick, and how to treat it, if you can. It's largely uniform.
But therapy is a lot more holistic and complex than that, it's all about who you are as a person, what you need as an individual, and how you need to pursue it in a way that's healthy and right for you. What could work for one person with, say, schizophrenia, may well not work for another, because they have different motives and goals, different personalities, and their schizophrenia may well not even manifest in the same way. The guy who hears voices telling him there's government bugs in his teeth is gonna need very different treatment to the woman who hallucinates extra members of the family telling her the whole family hates her. So the diagnosis informs something like 10%, maybe 20% of the treatment, you have to focus more on the specific client you're working with.
Then there's the second reason, which is much simpler, but a harder obstacle: in a lot of places therapists aren't generally qualified to give official diagnoses. Ireland is one of those places. That's something only a psychologist or psychiatrist can do, and only a psychiatrist can prescribe medications for that diagnosis. So while a therapist can agree or disagree with an assertion you make that you believe you have a given diagnosis, they can't diagnose you with anything. This is something i became painfully familiar with, since i've had 3 separate therapists confirm it appears that i have PTSD, but my psychiatrist never agreed with them, so i do not have a PTSD diagnosis. So there's no real point in them making unprompted claims you have a given diagnosis, and for the reasons i laid out in point one, they likely won't see much value in doing so - because it's possible it will only narrow your scope, when they want you to look at the bigger picture.
I hope all of that helped with maybe understanding where your therapist is coming from, and why they haven't broached the topic of a potential diagnosis with you. I also hope wherever this all takes you, it ends up being healing and constructive for you.
