The parent cannot assign the covenant because the child is baptised in the faith of the Church and not necessarily in the faith of the parents. Is the covenant between God and the baby binding? Yes. But, the covenant between God and the infant must be understood against the background of the covenant which can only be explained behind the theology of Original Sin, which is NOT an inherited stain on the soul from Adam and Eve's disobedience but, the ABSENCE of Sanctifying Grace because of Adam and Eve's disobedience. Then, it must also be viewed from the Biblical history of Divine covenants from Noah, Abraham, Moses, David so on and so forth simply because it fully explains why the covenant is literally and truly a fulfillment of God's binding oath of Divine blessings. If God's Divine covenant is understood on that basis, then it poses no problem in understanding why Apostolic Churches confer infant baptism because the Grace received during the rite of initiation into a faith community becomes a mark of familial unity with God.

Setting that brief theology aside, the question that remains would be in the matter of parental prerogative. Would it be contrary to the dignity of children as persons to impose on them future religious obligations that they may, perhaps later, be led to reject? I think the question we should really ask is: Is a child born with pure human freedom immune from being influenced in any way? Even on the natural level, parents make choices for their child that which are essential to that child's life and orientation towards his/her values. If the rite of initiation to any faith community is a means established by God to a bond of unity with Him, then, would'nt the child have an unquestionable right not to be prevented from receiving that Divine gift?