Backing up some for Paul's context:
1 Cor 15:12 (NASB) Now if Christ is preached, that He has been raised from the dead, how do some among you say that there is no resurrection of the dead?
Paul was teaching that there will be a resurrection and elaborates on it in the chapter. He also alludes to other "final" things, such as the coming of Christ, the last judgment, the turning over of the kingdom to the Father, the judgment of saints and sinners alike, and the beginning of "eternity".
Re: 1 Cor 15,
20But now Christ has been raised from the dead, the first fruits of those who are asleep.
21For since by a man came death, by a man also came the resurrection of the dead.
22For as in Adam all die, so also in Christ all will be made alive.
23But each in his own order: Christ the first fruits, after that those who are Christ's at His coming,
24then comes the end, when He hands over the kingdom to the God and Father, when He has abolished all rule and all authority and power.
V. 20: Paul reaffirms the resurrection of Jesus which is likened to a first harvesting of crops.
V. 21 (compare & contrast): Death entered into human history by the one man, Adam. By another man, Jesus, the resurrection from the dead had its beginning in human history. One brought death, the other life beyond death.
V. 22 (compare & contrast): Adam's disobedience introduced death which is experienced by all. Adam was as a "corporate head" of humanity in this sense. In the same way and as another corporate head; Christ, introduced eternal life into history by being raised from the dead.
V. 23: Paul specifies who will be resurrected to the eternal life that is in Jesus, the first to be raised from the dead. They are the "second fruits" -- the Christians "those who are Christ's at His coming". They, and they alone, are those who will be made alive unto eternal life.
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Paul doesn't specifically mention the resurrection of the ungodly in this chapter but he talks about their judgment. He does say that it was by Christ that resurrection was initiated into human history. This chapter is primarily teachings about the resurrection of Christ and of believers.
In the same book Paul demonstrates that not everyone will "be made alive unto eternal life":
1 Cor 6:9Or do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived; neither fornicators, nor idolaters, nor adulterers, nor effeminate, nor homosexuals,
10nor thieves, nor the covetous, nor drunkards, nor revilers, nor swindlers, will inherit the kingdom of God.
11Such were some of you; but you were washed, but you were sanctified, but you were justified in the name of the Lord Jesus Christ and in the Spirit of our God.
However, Paul does say a few things about the final judgment and destiny of God's enemies in:
1 Cor 15:24then comes the end, when He hands over the kingdom to the God and Father, when He has abolished all rule and all authority and power.
25For He must reign until He has put all His enemies under His feet.
26The last enemy that will be abolished is death.
27For HE HAS PUT ALL THINGS IN SUBJECTION UNDER HIS FEET But when He says, "All things are put in subjection," it is evident that He is excepted who put all things in subjection to Him.
28When all things are subjected to Him, then the Son Himself also will be subjected to the One who subjected all things to Him, so that God may be all in all.
At the Second Coming of Jesus, and before the kingdom is handed over the Father, every enemy of God will have been abolished. Every evil "rule, authority, and power"---and all who have aligned themselves with them will be put under subjection, judged, and destroyed. God will not "be all in all" until this is accomplished.
The means by which this will be done is the final judgment where all will be judged by Christ and rewarded according to their deeds: a. Believers---the inheritors of the kingdom---will receive rewards for obeying God which includes believing the Gospel. b. Unbelievers---the enemies of God who have no inheritance in His kingdom---will be rewarded in accordance with their evil, including their disbelief in the Gospel.
Therefore, the universalist interpretation 1 Cor 15:24 is incorrect, imo, because it:
a. lifts the verse out of context
b. reads 15:24b in a "wooden" & literalistic (incorrect) sense
c. doesn't take into account what the chapter teaches
d. [and what it doesn't teach] which has to be found elsewhere
e. doesn't acknowledge the fuller teaching of the rest of the book, and
f. doesn't take into account the fuller teaching of the Bible
In friendly debate, I wonder where's Danny?

Rick