My upgrade eligibility doesn't make sense

It shouldn't be saying you have to make payments towards/ pay off your current phone.  Most likely its trying to give you a calculation of what your next installments will be should you renew under the next plan most similar to what you have now.  

I see a few discrepancies in your message.  The iPhoen 6 was launched on Sept 19, 2014,  so it hasn't even been a full 2 years since that phone was released.  I'm not sure how you bought one "about 2 1/2 years ago" since it hasn't even been out for 2 years yet.

Considering that you are mistaken about when you purchased, perhaps you are also mistaken about if you have a NEXT upgrade agreement instead of a service contract.  Check your monthly bill and see if you have a section in there for "equipment".  I know I purchased my wife's and my iPhone 6 phones on launch day, and our Sept bill includes our last NEXT 18 installment, so the Spet 2016 payment is our 24th payment on our NEXT agreement, and the phones will be ours to do with as we please.  In fact my wife just went to an Apple Store and got hers replaced yesterday since we also purchased AppleCare+ for our phones, soo she has a phone that is as good as new right now.