Question: Why can’t you say the blessing over challah for others at any Shabbos meal if you aren’t eating challah yourself but you could say the blessing for vegetables at the Seder on Pesach for karpas even if you aren’t participating in it, for others?
A. The Mishna Berura says in (167:92) that the reason why one can say a blessing for someone else even to do a mitzva even if he himself already fulfilled the mitzvah is because “kol Yisrael areivim ze la’ze” we are all responsible for each other to do mitzvos so if one didn’t do a mitzva it is as if you yourself didn’t do the mitzva yet. However when just eating to eat, though one is obligated to say a blessing in order to eat and one cannot get pleasure from the world without a blessing but one can always choose to not eat and not need a blessing so the one who is not eating but would say a blessing for you is not considered obligated to say the blessing.
B. The Mishna Berura (273:19) says it’s not an obligation as a mitzva to eat challah at the 3 meals of Shabbos, rather if one wants to enjoy food on Shabbos he has an obligation to say a blessing on lechem mishna, two loaves of challah, but technically if he enjoys fasting he does not have to eat.
C. Karpas is only eaten to make the children ask questions and is not an obligation to be eaten.
Answer: The Dirshu Mishna Berura (484:1:4:4) quoting Rav Shlomo Zalman Auerbach says karpas is different because its main purpose is for a mitzva, of telling over the story of the Exodus and not for any enjoyment but lechem Mishna which is mainly for one to eat on Shabbos is considered for the sake of enjoying one’s food.