How come the New Testament contains major inconsistencies between its different gospels?

Because they're gospels according to ==Insert Disciple Name Here== and eyewitness accounts are always inconsistent (as well as unreliable). People see things through their own viewpoints and agendas and since most of them were written many, many years after Christ, memory gets dim and it is human nature to "fill in the blank spots" with supposed happenings. Get eyewitness accounts of an accident from 12 different people, and you'll get twelve different stories.