Question: According to Rashi (Brachos 48b) why should a man with only a rabbinic obligation to say Birkas hamazon because he only ate a kazayis of bread, is allowed to lead a zimun but a child who also has a rabbinic obligation to say Birkas hamazon (even if he eats to satiation) cannot lead a zimun?
A. The Torah obligation for Birkas hamazon is eating to the point of satiation as the Torah in Devarim 8:10 says, “And you shall eat and you shall be satisfied and you shall bless Hashem.”
B. The father has an obligation of chinuch to teach his children how to do mitzvos like bentching after eating bread.
Answer: The rabbinic mitzvah for a child to say Birkas hamazon is an obligation through the father, not his own mitzvah, therefore he cannot really lead a zimun. But the rabbinic mitzvah of one who ate a kazayis of bread is his own mitzvah therefore he is able to lead others who even have a Torah level obligation of Birkas hamazon, in a zimun.