I guess this is the answer:

Why Can't I Check-in Online:
https://www.cathaypacific.com/cx/en_...in-online.html

"This also applies for tickets issued on partner carriers where the partner carrier flight is the first sector for e.g.,
American Airlines: Dallas - New York
Cathay Pacific: New York - Hong Kong
In this case, you must check in on the partner carrier American Airlines flight first to be able to check in for the subsequent Cathay Pacific flight."

What a nightmare. So now I have to wait just 24 hours before my flight to get seats.