Our carnal man's burial "comparison" with the burial of Christ to be precise.
Paul is not talking about burying our carnal nature in that passage. In order to understand Paul's meaning, we need to pay attention to the questions he is answering.
What shall we say then? Are we to continue in sin so that grace may increase?
This rhetorical question follows from Paul's previous argument that God's grace is so extensive that he has forgiven us of all our transgressions. Our sins abound, but God's grace "super-abounds." Paul's objector will claim that Paul is promoting sin. If God's grace increased because our sin increased, and if this becomes a display of God's grace: then our sin glorifies God. And this conclusion proves that the gospel Paul preaches is false and Paul is a false teacher. Paul responds
May it never be! How shall we who died to sin still live in it?
Here begins Paul's defense against the claim that the gospel Paul preaches is a false gospel because it promotes sin. Paul will argue to the contrary, that his Gospel teaches us the true nature and penalty of sin.
Or do you not know that all of us who have been baptized into Christ Jesus have been baptized into His death?
From Acts chapter 19, we are now familiar with the idiom "baptized into", which means "immersed into the teaching of someone." Those who were baptized into John, for instance, were immersed in John's teaching. Those of us who have been "baptized into Christ Jesus" are immersed in his teaching. Therefore, Paul argues, why would anyone immersed in the teaching of Christ Jesus still live in sin? Those who are immersed in the teaching of Christ Jesus, learned about
his death.
Here is our first clue that Paul is NOT talking about death of self or the death of our carnal man. Though this teaching may be found elsewhere in the New Testament, that concept isn't the subject of Paul's point here. Paul isn't talking about OUR death; he is talking about the death of Christ Jesus -- what that means and why it was significant. And if we truly understood the significance of his death, we wouldn't want to continue in sin. We have been immersed in the teaching of his death, what it means, and why it is significant. Our death is not in view here.
Therefore we have been buried with Him through baptism into death, so that as Christ was raised from the dead through the glory of the Father, so we too might walk in newness of life.
Bear in mind, Paul is still defending the gospel in this context. And so, if we read this as a treatise on how to be saved, we will miss the point. Paul is not giving us practical advice about how to get saved. He is defending the teaching of Christ Jesus and why his followers are not likely to continue to sin that grace might increase. He isn't saying, "Okay now, get baptized so that you too might be buried with him." No. He is saying, "the gospel we believe tells us that Christ died on the cross in order to free us from sin and just as God raised Jesus from the dead, he is going to raise us from the dead also. This teaching motivates us to walk in newness of life. We are "buried with him" if we agree that we deserved to die on the cross rather than him; and if we agree that God favored his son and will grant his appeal on our behalf to save us from our sins.
For if we have become united with Him in the likeness of His death, certainly we shall also be in the likeness of His resurrection
It is a mistake to read this as if Paul is saying, "since we got water baptized we will be counted among those in the resurrection of the dead." This is not what Paul has in mind. Notice his use of term "likeness" to describe the death of Christ Jesus and his resurrection. The followers of Jesus are not hoping for a "likeness" of his resurrection; they are hoping for actual resurrection. Therefore, Paul is not speaking about actual resurrection; he is speaking about the likeness of resurrection.
In other words, when I enter into new life to become a follower of Jesus through the rite of water baptism, I picture my own death to sin, having employed a visual picture of burial, which is likened to Jesus actual burial in the ground. Then, when I emerge from the water, I have employed a visual image of my future resurrection when, at that time, I will be not only free of the penalty of sin; I will be free of sin itself, no longer to sin ever again. Since my hope is set on that day, when I get out of the water, I am committed to living in the light of that hope, walking in newness of life.
What is the point of this? Paul is arguing that the followers of Jesus are motivated to avoid sin, not to increase in sin, based on what they believe about the necessity of the cross and the significance of the cross as it relates to both Jesus and his followers. Why would someone who hopes to be set free from sin continue to live in it?