I think it is because your route end up LAX - xHKG - oICN - oTPE - xHKG - LAX if you travel CX all the way, which LAX xHKG ICN is beyond the 60K AM mark or they need to do on 2 redemption ticket because of redemption limit (i.e. LAX - HKG - LAX + HKG - oICN - oTPE - HKG)
You should call AM to have a ticket book like this
LAX - ICN (AA)
ICN - TPE (CX)
TPE - LAX (AA)