The bronze-colored, er, tip thing is the nozzle assembly. Iwata refers to it as the fluid nozzle for reasons beyond me.
Anyway, as somebody mentioned above, it is typical for this part to get stuck, though it usually gets stuck in the nozzle cap, not the airbrush body as yours is. In fact, if I'm not mistaken I think Don may allude to this stuck part in his review of the airbrush (on Don's Airbrush Page), also mentioned by somebody above.
In both cases (nozzle vs nozzle cap or nozzle vs airbrush body), it is a taper fit and the problem is caused (or at least augmented) by overtightening the nozzle cap. I never even use the little wrench Iwata supplies. Finger tight works for me.
I agree that a long soak in something (lacquer thinner, maybe) might work. I've done that. What works more reliably for me is 5-10 minutes in an ultrasonic cleaner, though folk might scold me for putting the whole body in there.
I gave up once when the nozzle was stuck in the nozzle cap (not what you have here) and bought a whole new nozzle assy and nozzle cap, so you are not all alone or the first person this has happened to.
I know it's frustrating as all get out, good luck.
On a side note, yet again my apologies to my friends who posted above, but whose posts I cannot see whilst I compose this reply. My memoery just isn't good enough to remember who said what up there, and it is too bad we can only see 1 post above. Ahem. Ahem. Wink wink nudge nudge say no more.