Why would some people want, need, choose or have to believe that Jesus Christ is still offering Himself to God His Father, in His "Sacrifice of the Cross"?
Becasue He is. Offering is what it means for God the Son to be God the Son. Revelation 5:6:
"Then I saw a Lamb, looking as if it had been slain, standing at the center of the throne, encircled by the four living creatures and the elders. The Lamb had seven horns and seven eyes, which are the seven spirits of God sent out into all the earth." Who is the lamb?
What happened at calvary-----is-------an earthly projection of a heavenly reality. God the Son is taking divine reality----that happens from eternity-----and translating that reality into something we can comprehend and understand from our earthly perspective. What makes the cross unique is NOT the offering itself---but in the MANNER of offering. When Christ offered Himself on the cross-----he did so---in his earthly flesh---stripped of heavenly glory. Christ did so as one of us--which meant--He experienced suffering, pain, and death. In so doing--God entered the full consequences of Sin----and in bringing God to those consequences, turned them on their head. Now, they become the means of life, glory, and perfection. Now they become redemptive.
The Resurrection is the cross. This is the whole problem with Protestants---they do not recognize the resurrection as one and the same cross. They think of it as disconnected from the cross---and substantively different from the cross. The resurrection is what the cross--that is--the offering of Christ looks like when perfected--glorified. The resurrection allows Christ to offer Himself-----------without pain, suffering, and death. The resurrection is what the cross looks like-----joined to heavenly realities--that is--when earthly flesh is transformed and perfected.
Thus, the offering itself is eternal. The MANNER of offering on the cross UNIQUE. That happened once, for all. It is not repeatable. Christ suffering and died ONCE for the sins of the world. Now, Christ offers himself day and night unto the Father and lives to make intercession for us---without suffering, pain, and death.
"Once I was dead, but now I live, forever and ever." The Mass is the presentation of this offering--that is--we encounter the offering---in its glorified and perfected form. Christ offers Himself in the Mass--but does not suffer, experience pain, or die. The Mass is a presentation of one and the same offering---but the MANNER in which Christ offers Himself is what is different. Christ, in the Mass, offers Himself in a non-bloody, non-fleshy way.
Why does the Roman Catholic Church preach and teach that Jesus Christ in His Sacrifice of the Cross to His Father, is still being continued now,
Becasue it didn't begin on the cross and did not end on the cross.
by way of a staged man-made presentation that is orchestrated and performed each and every day in the Roman Catholic Church.
The Mass is neither "staged," "man-made," or "orchestrated." The Mass is our divine worship of God the Father with, though, and in Christ. In the Mass, we offer ourselves together with Christ--to God the Father as the perfect work of the Son.