For we were buried with him by means of Baptism into death, in order that, just as Christ has arisen from the dead through the glory of the Father, so we also may walk in newness of life.
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Just a quick comment. Paul here explains, although that is not the focus of his comment, another reason why "things happened the way they did" and that Jesus "was not just another prophet or holy man." I mention those kinds of thoughts because modern day skeptics often miss the obvious and thus weaken the faith of those who listen to their doubt whispers.
Paul wisely understands that Jesus is demonstrating to each person the steps of life and faith with his own body. None of the prophets demonstrated the reality of God and heaven by actually dying and being resurrected by God. Previous prophets were taken up into heaven while they were still alive. But only Christ, through God's power and glory, demonstrated both the spiritual steps of life, death and resurrection but also their physical reality, through his own body. God sent Jesus as the Son to demonstrate the faith through miracles, his preaching and his fulfillment of scriptures (such as being born of the Virgin Mary), but also to demonstrate the faith through being baptized, living the faith, dying, and then demonstrating that death is not the end. God allowed Jesus to suffer and die and then absolutely and not symbolically but in the flesh, come back to life to show the newness of life. Jesus did this unmistakably by resurrecting in his body still bearing the nail and lance wounds, that could be seen and felt, so it is indeed truly him alive and not a spirit, yet he gives a "preview" of what each human's glorified body will be, since Jesus was able to move this body in the spiritual realm, suddenly appearing through locked doors and into rooms.
So in this passage Paul is explaining that Jesus provided a road map that he actually shares the walking of with each human being. Therefore while Paul is focused in this passage on the newness of life being reborn in the faith, with then the opportunity to glorify God in this life and forever, he also gives the reader the message that Jesus also walked those physical steps to death and beyond, in order to glorify God and strengthen the faith and belief by humankind.