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Pidyon ha-ben is the mitzva for a father to redeem his firstborn son on the thirtieth day following his birth, by giving money to a priest (Kohen). Why? During the last of the ten plagues, the slaying of the firstborn, God killed all the firstborn Egyptians but spared the firstborn Israelites. As a result, the firstborns were singled out to be priests. Thus, every tribe and every family would have holy people who would behave piously and serve as teachers and role models. Unfortunately, this plan failed, as the firstborns did not prevent the sin of the golden calf. It was clearly necessary to dedicate an entire tribe to the task of perpetuating sanctity among the people. All the members of this tribe would view this as their holy mission. God chose the tribe of Levi, since they had not participated in the sin of the golden calf. Nevertheless, since firstborns had originally been singled out to be priests, the Torah requires a father to redeem his firstborn son by paying money to a priest.
We can extrapolate from this mitzva that every firstborn starts off with sanctity, presumably because his birth begins the next generation. However, in practice it is difficult to actualize this sanctity, since the excessive responsibility often imposed on firstborns may incline them to be high-strung and arrogant. Therefore, the firstborn should be redeemed, enabling him to live a normal life in which he can find his own way with modesty and moderation.
