Rashi explains that in the case of minors there is an assumed reservation for the korban of their parents or guardian. It’s not a retroactive reservation, but rather it’s as if the reservation was made before the shechita.
Tosfos, however, connects the sugya with R’ Zeira’s din (Nedarim 36) that “she l’bais avos lav d’oraysa,” that the din of minuy does not apply to ketanim. There is no proof to the issue of breira because nothing happens retroactively here – a katan’s reservation does not count for anything. (See R' Chaim in Hil Korban Pesach for a discussion of this point.)
That solves the issue of breira, but it does not explain how the katan can eat the korban. If he has no reservation, and a korban can only be eared “l’menuyav,” how is he allowed to eat? How are we allowed to feed him the food? Just as we learn in our parsha that there is a din “l’hazhir gedolim al haketanim” to cause a minor who is a Kohen to become tamei, there is an issur to feed ma’achalos assuros to a child as well. If a katan cannot reserve a portion, how can we feed him the korban meat?
Ran (Nedarim 36) answers that since the whole concept of minuy does not apply to a katan, there is no issur of a katan eating without minuy. Tosfos offers a different solution. Even though a korban may only be eaten by those who have reserved in advance, when it comes to a katan we waive the requirement for the sake of the mitzvah of chinuch.
One might have argued that the whole issur of feeding ma’achalos assuros to a child does not apply here because it’s not that the korban is like treif food – there is simply a mitzvas aseh for the katan to make a reservation that has not been fulfilled. You see a chiddush from Tosfos’ question that the issur of lo ta’achilum, of giving ma'achalos assuros to a child, is actually very broad in scope.
R’ Moshe Brown in his sefer Ma’adanei Moshe points out that the Ran in the end of Yoma also seems to understand the issur very broadly. If the inuyim of Yom Kippur are d’orasya (as the Rambam paskens), asks the Ran, how can the gemara allow a child to be washed? Here too, the inuyim of Yom Kippur are a fulfillment of a mitzvas aseh of “v’inisem es nafshoseichem,” not a lav. Even if one assumes that an issur aseh should be treated like a lav, it could be that those who argue with the Ran hold that “v’inisem” is simply a mitzvah kiyumin like wearing tefillin or shaking lulav. There is no problem in these cases of causing a katan to not fulfill the mitzvah.