Hopefully, these Catechism references will help clarify. It is the Divinity united to humanity in the Person of Jesus that makes the cross of Christ redemptive for mankind. This is why it is perfectly appropriate to offer the Divinity back to the Father. Also, keep in mind that the offering is not necessarily suffering, as was indicated in another post. The offering is the sacrifice of love and obedience. As noted by another posted, even the Incarnation was a sacrifice of love, but it was just the beginning. As an aside, we also make this offering at the Mass when the Eucharist is offered back to God as the memorial sacrifice of the Son.
464 The unique and altogether singular event of the Incarnation of the Son of God does not mean that Jesus Christ is part God and part man, nor does it imply that he is the result of a confused mixture of the divine and the human. He became truly man while remaining truly God. Jesus Christ is true God and true man.
616 It is love "to the end"446 that confers on Christ’s sacrifice its value as redemption and reparation, as atonement and satisfaction. He knew and loved us all when he offered his life.447 Now "the love of Christ controls us, because we are convinced that one has died for all; therefore all have died."448 No man, not even the holiest, was ever able to take on himself the sins of all men and offer himself as a sacrifice for all. T**he existence in Christ of the divine person of the Son, who at once surpasses and embraces all human persons, and constitutes himself as the Head of all mankind, makes possible his redemptive sacrifice for all. **
618 The cross is the unique sacrifice of Christ, the “one mediator between God and men”.452 But because in his incarnate divine person he has in some way united himself to every man, “the possibility of being made partners, in a way known to God, in the paschal mystery” is offered to all men.453 He calls his disciples to “take up [their] cross and follow [him]”,454 for "Christ also suffered for [us], leaving [us] an example so that [we] should follow in his steps."455 In fact Jesus desires to associate with his redeeming sacrifice those who were to be its first beneficiaries.456 This is achieved supremely in the case of his mother, who was associated more intimately than any other person in the mystery of his redemptive suffering.457
1374 The mode of Christ’s presence under the Eucharistic species is unique. It raises the Eucharist above all the sacraments as “the perfection of the spiritual life and the end to which all the sacraments tend.” In the most blessed sacrament of the Eucharist “the body and blood, t**ogether with the soul and divinity, of our Lord Jesus Christ **and, therefore, the whole Christ is truly, really, and substantially contained.” …
1357 We carry out this command of the Lord by celebrating the memorial of his sacrifice. In so doing, we offer to the Father what he has himself given us: the gifts of his creation, bread and wine which, by the power of the Holy Spirit and by the words of Christ, have become the body and blood of Christ. Christ is thus really and mysteriously made present.
