Were there connecting flights involved? Was your flight booked with DL flight number or as a codeshare number?

Do you know if other passengers were connecting?

I know of two ways this duplicate seat issue could happen (not that there aren't others, just these are two I've seen most) -

1. One set of passengers are connecting from international flight from LHR/CDG/AMS/etc where one carrier handles other flights using their own systems. If passengers get rebooked (IRROPS) by DL once international flight is under control of OAL, the connecting flight seat map can become "disconnected" for lack of better word from reality. Passenger will get a BP and otherwise look great. The BP will show a seat number. However the passengers seat assignment isn't being done on the actual flight seat map. Instead the system is handling the seat map as if the OAL was also controlling the connecting flight. I've seen this happen when co-workers rebooked from a DL flight from both AMS and LHR to another DL flight. I've also had it personally happen when at AMS was rebooked from a DL flight to AM (KL also handles AM). In all the cases we all had called DL in US to rebook. KLM issued the BP for both flight from AMS and connection. Nothing appeared wrong. It wasn't till got to gate and went to board we realized issue. Them at their DL connection and me at my AM connection. They removed the duplicate passenger (we were paid) and then would go and try and place us in the seat. It would act like it did it, a new BP would print out. When they looked at their seatmap, it would show it still as empty. GA had to basically rebook us onto the flight again. No matter what they tried till did that worked.
2. The other issue I've seen is when agent applies a GUC/RUC when the marketing of flight doesn't allow. A DL operated flight must be sold as a DL/AF/KL/KE/AM/or VS flight number to use a RUC/GUC. If Agent tries to upgrade a say LA flight number it'll cause issues. The way they try and force the upgrade is the issue. There is a way an agent willing to break the rules can do this without breaking everything. However most wouldn't know this.

Sadly this is result of having systems running on software made decades back.