This is a rather puzzling segment of Paul's letter and it is good to be reminded that he is writing to answer the letter from the church at Corinth, so it is difficult to understand without the context which having that letter would bring.
It is likely that in the Early Church their grew up a custom which revealed a rather superstitious attitude towards baptism. It began to be regarded by some that a person who died perhaps as a newly converted believer who hadn't had the opportunity to get baptized, would be excluded from eternal life. To prevent this, a volunteer would be baptised in place of the person who had died in order to ensure their eternal salvation. Here Paul neither approves nor disproves of this action; instead he uses the fact of the practice to support his assertion of the resurrection from the dead.
As Paul says, what is the point of being a Christian and facing, probably in the days of this letter being written, the low level persecution believers faced if there is no resurrection? As recorded in the book of Acts, Paul faced much more intense persecution and the worst appeared to have been in Ephesus (Acts chapter 19). It is highly unlikely that Paul, a Roman citizen, would have been forced to fight animals, rather he describes here his attacks by human animals, behaving with hatred.
So Paul declares that, if the thought of the life to come is taken away then why bother keeping to a certain moral standard? Why not, and here he quotes the words of Jesus in Luke 12 v 19, do whatever you feel like? Paul insists then that dismissal of the Christian hope in a glorious afterlife is a sign of ignorance of God and brings its own degradation.