T he   קרבּן פּסח   was supposed to be eaten by a group.  That's why we specifically invite people to join us on pesach. First they would eat the חגיגה, which is why we first say  ייתי ויכול , and then for dessert they ate the קרבּן פּסח, which is why we say 

ייתי ויפסח second. 


haggadah Section: Maggid - Beginning