The Fast of the First Born was instituted for the day before the first Passover Seder.
I have an older brother, so I'm not obligated to fast then. But my first child was a son, and he is obligated to fast. Of course when he was only a few years old he did not fast.
According to an article at Wikipedia:
Many authorities, including the Rema, note the custom that the father of a firstborn should fast on his child's behalf until the child reaches halakhic adulthood. The Rema rules that if the father is a firstborn himself, the mother should fast on behalf of the child. The Mateh Moshe and Maharil dispute this and rule in such a scenario that the mother need not fast. The Magen Avraham rules that it is appropriate to follow the lenient opinion if fasting causes the mother excessive discomfort or if she is pregnant or nursing, but he adds that a mother who begins following the former opinion must maintain that custom and fast in subsequent years.
This seems pretty unusual.
I realize that there are commandments (like circumcision or redemption) which the father normally does for his son, and which the son would otherwise have to do for himself eventually. But this fast doesn't seem like that. If nobody fasts on behalf of a child, those neglected fasts aren't hanging over the child's head, waiting for him to reach adulthood and perform the fasts of his first 12 years of life.
Also, I suppose, if a father won't circumcise or redeem his son, someone else could do it instead. The fast is not just an obligation hanging over the community, like offering hospitality to guests. It's not that someone must fast, and if a firstborn child cannot fast then someone else should. It seems that particularly the father (or mother) should. I realize that during the plague of the firstborn, the Jewish parents must have been happy that their children lived. Younger siblings might have been happy too, and parents of firstborn adults, and lots of other people might have been happy. So I feel like there's something missing from that reliance on natural feelings.
It seems that with respect to commandments in general, a child is simply exempt. Nobody has to perform any of the commandments for him, during his childhood or later, that he fails to perform as a child. Why don't we make that subjective analysis in the case of other commandments? Why is this one special?