I just booked and flew on SNN -> JFK -> SFO through Aer Lingus and had the same problem.

Unfortunately I think the problem is actually with Aer Lingus, and is pretty crazy!

SNN - JFK was Aer Lingus and JFK - SFO was Jet Blue. I booked through Aer Lingus and booked business class. Nowhere in the process did it indicate that any part of the booking was economy.

I couldn't select a seat on Jet Blue flight so I called them. They said I was in economy. I called Aer Lingus, got disconnected after half and hour, called again for another half hour. They said that there is nothing they can do, and that this is company policy and that they cannot guarantee business class on codeshares, despite there clearly being business class seats available on the jet blue flight. They also said they couldn't upgrade me even if I paid more.

I called Jet Blue and they also couldn't upgrade me if I paid, as Aer Lingus had issued the ticket. They were great, though. I would really recommend them.

Luckily when I arrived in JFK I was able to pay for an upgrade at the gate, though this cost ~$400.

It's unbelievable that Aer Lingus do something so incredibly misleading and wrong. I will definitely never, ever be flying with them again.