It must have come as a shock to Number 2 to discover that he is 'C', poor old chap! The trouble was he was put under extreme pressure by Number 1, and for no good reason as far as I can see. His own personal problem was, he underestimated Number 6, and at the end was all too keen to get his twin on the wall screen to open the envelope the Prisoner had handed him, he just had to see what was in it. Number 6 was playing Number 2 for a fool, he wasn't selling out, he really was going on holiday!
Footnote: To think that this Number 2 had gone to all the trouble of researching and computing the Prisoner's whole life, and the computer never even considered the fact that the Prisoner might have been going on holiday - even Number 2 of 'Arrival' was aware of that fact!
Be seeing you