First, notice that Paul does not say the only thing he would preach was Christ and the crucifixion, as some have assumed; he says the only thing he would know among the Corinthians was Christ, the One crucified. The Amplified Bible renders it this way: "For I resolved to know nothing (to be acquainted with nothing, to make a display of the knowledge of nothing, and to be conscious of nothing) among you except Jesus Christ (the Messiah) and Him crucified."
Looking at the audience (the people of Corinth were Greek) and the verses preceding this one, it is clear that Paul's intent is not to be distracted by extraneous topics that the Corinthians might have been more inclined to listen to. His statement in verse 2 ties back to two different themes before it:
For it has been declared to me concerning you, my brethren, by those of Chloe's household, that there are contentions among you. Now I say this, that each of you says, "I am of Paul," or "I am of Apollos," or "I am of Cephas," or "I am of Christ." Is Christ divided? Was Paul crucified for you? Or were you baptized in the name of Paul? (I Corinthians 1:11-13)
At the beginning of the letter, we see that Corinth seemed to be more focused on the human leadership than on the Messiah. Paul's statement in I Corinthians 2:2 gives an answer to this. He says, in effect, "I'm not going to be focused on myself, or on any other servant of God; I'm going to be focused on God Himself."
The second theme starts in I Corinthians 1:18 and goes through the end of the chapter. Paul is addressing something else the Corinthians were dealing with: The Greeks are renowned for their love of human wisdom, philosophy, metaphysics, and debate, as well as a religious system of multiple gods and goddesses. To such a mindset, the fact that a God would not only submit Himself to a lower (human) form, but also die for the very people He created, was unthinkable! This is why Paul says in I Corinthians 1:23, "But we preach Christ crucified, to the Jews a stumblingblock and to the Greeks foolishness." The God of Christianity, and the whole Christian system, did not make any sense to the Greek philosophers, intellectuals, and theologians.
Paul contrasts the Greek ideals, which were largely humanist, with the godly ideals. In I Corinthians 1:26-29 Paul shows that God is not interested in what the Greeks (or mankind in general) were interested in; instead, He called the weak, the base, the foolish things of this world to confound the wise, the mighty, the noble - those that the Greek world certainly would have been holding in high esteem. Paul continues this thought in I Corinthians 2:1, where he says he did not come to the Corinthians with "excellency of speech" or "wisdom" - again, things the Greeks regarded highly. Instead, as verse 2 says, he came to "know" Christ among them and Him crucified.
It is evident from Paul's letters to the Corinthian church, as well as his other writings, that the life and death of Christ were not his only topics. I Corinthians 5 explains the defilement of immorality. Chapter 6 deals with working things out among the brethren rather than taking matters to a civil court. Chapter 7 contains principles of marriage. Chapter 8 covers not defiling the conscience. Chapter 9 speaks of service and self-denial. It is easy to see that Paul wrote on a great deal more than just the life and death of Jesus Christ - they were just the starting point for his instruction. With Christ's sinless life and willing self-sacrifice comes remission of our sins, and justification - being brought into alignment with God and His inexorable law. Once we have been forgiven and have entered into the New Covenant, our responsibility becomes focusing on the Christian walk and conforming our life to the life of Christ. This is where all of Paul's instructions on "Christian living" come into play.
The ultimate reason for this is that the gospel message is not just about our forgiveness of sins through Christ's sacrifice. The gospel is also about the soon-coming Kingdom and government of God. The scriptural evidence that the Kingdom is a foundational part of the gospel is overwhelming:
In those days John the Baptist came preaching in the wilderness of Judea, and saying, "Repent, for the kingdom of heaven is at hand!" (Matthew 3:1-2)
From that time Jesus began to preach and to say, "Repent, for the kingdom of heaven is at hand." (Matthew 4:17)
And Jesus went about all Galilee, teaching in their synagogues, preaching the gospel of the kingdom, and healing all kinds of sickness and all kinds of disease among the people. (Matthew 4:23-24)
For assuredly, I say to you, till heaven and earth pass away, one jot or one tittle will by no means pass from the law till all is fulfilled. Whoever therefore breaks one of the least of these commandments, and teaches men so, shall be called least in the kingdom of heaven; but whoever does and teaches them, he shall be called great in the kingdom of heaven. For I say to you, that unless your righteousness exceeds the righteousness of the scribes and Pharisees, you will by no means enter the kingdom of heaven. (Matthew 5:18-20)
But seek first the kingdom of God and His righteousness, and all these things shall be added to you. (Matthew 6:33)
Not everyone who says to Me, 'Lord, Lord,' shall enter the kingdom of heaven, but he who does the will of My Father in heaven. (Matthew 7:21)
Then Jesus went about all the cities and villages, teaching in their synagogues, preaching the gospel of the kingdom, and healing every sickness and every disease among the people. (Matthew 9:35)
The Son of Man will send out His angels, and they will gather out of His kingdom all things that offend, and those who practice lawlessness, and will cast them into the furnace of fire. There will be wailing and gnashing of teeth. Then the righteous will shine forth as the sun in the kingdom of their Father. He who has ears to hear, let him hear! (Matthew 13:41-43)
And this gospel of the kingdom will be preached in all the world as a witness to all the nations, and then the end will come. (Matthew 24:14)
Now after John was put in prison, Jesus came to Galilee, preaching the gospel of the kingdom of God, and saying, "The time is fulfilled, and the kingdom of God is at hand. Repent, and believe in the gospel." (Mark 1:14-15)
This is just a small sample from Matthew's account (with an additional verse from Mark to demonstrate what Christ preached) - and it does not even include the parables, the vast majority of which were about the Kingdom!
Paul also wrote a considerable amount about the Kingdom, even to the Corinthian church (I Corinthians 4:20; 6:9-11; 15:20-25; 15:50; Galatians 5:19-21; Ephesians 5:5; II Thessalonians 1:3-5; II Timothy 4:1-2; Hebrews 12:28-29). James also spoke of inheriting the Kingdom in his epistle (James 2:5), as did Peter (II Peter 1:10-11).
In the face of all of this evidence, it is clear that the soon-coming Kingdom of God, which will be ruled by Jesus Christ on earth (Zechariah 14:3-5, 9; Matthew 5:5, Revelation 5:10; 20:4-6), was certainly a significant part of what Jesus Christ preached, as well as what Paul wrote about. The gospel is not about Christ or the Kingdom; it is about both. It is the good news that a relationship is available with our Creator, on the basis of a sinless life sacrificed on our behalf, but that is only the beginning. The Kingdom is what we are striving for - living eternally with God, and as He lives - but it is evident that not all will make it into the Kingdom. Men have rejected, and continue to reject, the law of the King, and in doing so they signify that they do not want to be ruled by God (Romans 8:7). The perfect work that Christ did is really just the starting point. It allows for the relationship with God to start, but it also obligates us to respond to God in submission and obedience. God is not going to have someone in His Kingdom who will not be ruled by Him! It is our responsibility to begin living now as we will be living in the Kingdom.
This is why Christ and John the Baptist specifically link repentance with the Kingdom of God. Repentance is a wholehearted turning from the ways and acts which caused our Lord to have to be crucified. The first part of repentance is determining what sin is: "Whosoever committeth sin transgresseth also the law: for sin is the transgression of the law" (I John 3:4, KJV). It is our transgression of the law which caused Christ to have to die for us. Now that our sins have been forgiven, are we free to live in sin (iniquity, lawlessness) again? "What shall we say then? Shall we continue in sin [shall we continue to transgress the law] that grace may abound? Certainly not! How shall we who died to sin live any longer in it?" (Romans 6:1-2). Part of our obligation is to determine from God's Word what is the right way to live, the way that is in alignment with God and not enmity against Him (Romans 8:7). God has codified this right way to live in His law; it is up to us to follow through with it!
To focus only on the crucifixion of Christ, to the exclusion of His teachings and examples, as well as the instructions contained in the rest of the Book, is to fail to understand the depth of what God is doing. To leave Christ hanging on the cross, as it were, is to emphasize our forgiveness above what is then required of us.