Ok, well, I don't believe the issue is as simple as people often make it out to be. Adam and Eve eating from that other tree God strictly prohibited them from is what brought about spiritual death, as sin and the very knowledge of it entered the world because of it. This is why God promised their death in the day they ate from it. Its crystal clear that God cursed the earth, pretty self explanatory. But its peoples interpretation of the curse of physical death and its relation to spiritual death that I have an issue with. Its often claimed that spiritual death is what brought about physical death, yet that clearly doesn't fit the narrative presented in Eden.
If this were really true, God wouldn't have been so concerned about their access to the tree of life afterwards to start with, since their spiritual death would makes their physical death inevitable regardless. If by "spiritual death" they mean separation from God, then it all begins to make a ton more sense. It explains why God told Moses he would die if he saw his face for instance. But when it comes to the body itself, its pretty clear to me from Jesus's explanation of the promised "glorified body" that he could have designed our bodies with immortality to begin with, if he really wanted to. He didn't, because he knew what was going to happen and planned accordingly, he is no moron.
At no point is the body itself ever explained away as the reason why we will attain sinless perfection. The spiritual component of the soul is an entirely different matter than the body. Its expected that scriptures like Romans 5:12 will be quoted as a "rebuttal", but exegesis is supposed to be all about consistency. If sin in itself brings death, then Satan would have dropped dead long ago. He certainly wouldn't have been up there in heaven accusing Job of being a turncoat to Gods face. Him being able to stand before God as a sinful angelic being just shows that "spiritual death" is a more complex matter than typically assumed when it comes to humanity. "Spiritual death" leads to physical death, but only for us, and only in the very presence of God Almighty, because we are living souls. He wants a real relationship with his image bearers, and it will not happen as long as sin exists.
A big long response to a simple answer to a simple question!
The simple answer that Adam's disobedience brought the curse upon the world and mankind. The reason why Jesus died on the cross was to bear God's wrath and the curse, and to take upon Himself the penalty for our sinfulness, which was part of the curse on us. The Scripture says, "Cursed is he who hangs on a tree". When Jesus cried out, "It is finished", it meant that He paid the whole "fine" that we would have had to pay at the judgment. But when we stand before God at the Judgment, He will say, "Your fine has been paid. You can go free".
That is why we have to make it quite clear to an unsaved person's conscience that because he has broken the Ten Commandments he is under God's curse and therefore will be condemned at the Judgment. When he realises that, and says, "What shall I do?" Then you can show Jesus coming to died on the cross to take that curse off him and that there will be no penalty to pay at the Judgment.
This has been the most effective way of people turning to Christ through the preaching of the gospel. Peter did it on the day of Pentecost. He hit their conscience and they were "pricked at the heart". Paul did the same to the Romans, especially in Romans 1-3 when he clearly pointed out that "All have sinned and come short of the glory of God". He told the Greeks in Athens that their "Unknown God" was the creator of the world and He has commanded all men everywhere to repent. Jesus hit at the conscience of the rich young ruler who thought he was keeping all the commandments, but had his coveting revealed to his conscience, after Jesus telling him that no one was good except God, and that included the young man. Jesus also hit to consciences of His listeners when He said that even if a person hated another in his heart, he was a murderer, and if a man looked on a woman with lust, he was an adulterer at heart. All of His listeners would have been reminded when they had hated someone, or looked with lust at a woman, and would know in their conscience that they were murderers and adulterers at heart in the sight of God.
What Jesus did in His teaching was to show the unconverted Jews that they were sinners through His preaching of the Law, and that they needed something more than the blameless observance of the Law as demonstrated by the Pharisees.
In fact, Jesus preached the Ten Commandments, so did Peter and Paul, and that was the reason why they succeeded in the Roman Empire turning from paganism to being Christianized through the first three centuries until Constantine made it official that the Roman Empire was now Christian.
The reason why we can't turn our societies to Christ is because we are preaching a Jewish oriented gospel to a world of neo-pagans who don't have a Biblical world view any longer.