I was suggesting using ITA Matrix to find current fares (and the fare rules for infants <2 without their own seat). When I posted your picture in post #566 didn't appear. It looks like you determined infant fare pricing directly from CX. Looking at the fare rule for:

Cathay Pacific (CX) IXNYC NYC to BKK

ITA Matrix shows that infant fares are charged at 10%.

Category 19: Discounts
ACCOMPANIED CHILD 2-11 - CHARGE 75 PERCENT OF THE FARE. TICKET DESIGNATOR - CH AND PERCENT OF DISCOUNT OR - UNACCOMPANIED CHILD 6-11 - CHARGE 100 PERCENT OF THE FARE

OR - 1ST INFANT UNDER 2 WITHOUT A SEAT - CHARGE 10 PERCENT OF THE FARE.

TICKET DESIGNATOR - IN AND PERCENT OF DISCOUNT OR - INFANT UNDER 2 WITH A SEAT - CHARGE 75 PERCENT OF THE FARE. TICKET DESIGNATOR - CH AND PERCENT OF DISCOUNT.

Now, that fare prices the adult at 4,707.10 one way in Business. I'm not sure how it's pricing at $13,303+ on your screenshot. The infant seat will be priced at xx% of the available adult fare at time of booking. Don't wait too long to book the infant fare - you may find only non-discounted J fares available.