I'm having a difficult time with the accounts in Matthew/Mark vs Luke at the Last Supper. My first assumption is all four gospels are written chronologically - meaning the events are written in order (A happened, then B, then C).

Matthew 26:21-25 has Jesus declaring and condemning a betrayer. Then the institution of communion. Then the "won't partake" statement after communion.

Mark 14:18-21 is exactly the same (except for slight wording and the absence of Judas asking if he is the betrayer as is in Matthew) - communion is instituted and then the "won't partake" statement afterward.

Luke, though, presents the "won't partake" statement BEFORE communion and Jesus declares and condemns the betrayer AFTER communion.

My question is: how is it possible to reconcile these specific details in the three gospels, while still maintaining the individual timelines? Most harmonies I've looked at simply adopt one timeline from Mark, Matthew or Luke, then plug in the other gospels to make it fit.

I thought inerrancy meant there was no incorrect information in the bible - that it was perfect? If all four gospels are chronological, how could all four timelines be correct? Specifically, how can Matthew/Mark be correct while Luke has these events in opposite order?

Thanks for any help.