Why would CX know anything about availability with another airline? If you are asking to change your flight they will provide you with the availability they have in the class of travel you have purchased or provide you with an alternative. Also Cathay Pacific do not have First Class to Auckland so your theory is flawed.
CX have no show fees but as long as you inform you aren’t going to take the flight the fee is waived, the no show fee is used to discourage people from not informing the airline so in turn it can sell on the extra seat. CX routinely overbook flights, they also codeshare on the route you mention with ANZ it maybe there allocation of seats on your selected flight had been oversold.
I’ve changed numerous flights with CX and I’ve never had a problem, I’ve always found their change policy to be very lenient compared to other carriers