From my understanding of the proof that halting problem is not computable, this problem is not computable because if we have a program P(x) which computes if the program x halts or not, we got a paradox when giving P as an input to the same P, having: P(P), trying to decide if P halts or not using P itself.
So my question is: is halting problem computable by program P for all other programs used as input but P itself? In other words: is halting problem not computable only in this special case or the proof is more general and I'm missing something?