Misdiagnosis Frustration

My son, age 33, has psoriasis - much worse than mine ever was, unfortunately. He gets patches on the back of his head, eyebrows, his nose, under his beard, on his forearms, knees, ankles, and chest. It's obviously psoriasis, with heavy flaking, itching and stinging. About a year and a half ago he also started experiencing joint pain and fatigue.
He moved to my area over the summer and I made an appointment for him with my dermatologist with the hope of getting him started on Skyrizi, which has been a game changer for me. And with that, maybe it would prevent worsening joint damage.
My current dermatologist was not the one who diagnosed me - I was already on Skyrizi when I started seeing him after moving here two years ago, but he seemed fairly well-versed on both psoriasis and PsA. I also told him about my son at my appointment in June.
Yet he told my son he has eczema, NOT psoriasis and would not prescribe anything! Eczema is nothing like psoriasis, looks nothing like it, and there's obviously is a history of psoriasis, which I'm being treated for by this same doctor. How does a trained dermatologist not know the difference between the two??
I'm floored, and beyond frustrated. Obviously we'll have to find another dermatologist (and pay for another $250 visit), and hopefully find one who has some common sense. While psoriasis isn't the easiest thing to live with, I'm most concerned about preventing the joint damage I'm living with, so he doesn't have to. Unfortunately, rheumatologists with PsA experience are very rare in this area, so dermatologists are the best bet.
But eczema? Really???