What is a generation curse? There has been a lot of confusion around this idea, because it sounds more supernatural than it was meant to be taken. Simply put, when a father has a destructive (sinful) lifestyle, his children are likely to practice the same. That is all.
Just as some churches today took this theology further than it was intended, the religious group in Jesus' day took this to the extent that people were being pushed out of society.
The topic of generational curse has been a controversial one since the days of Jesus. As a matter of fact, the author of the book of Mark places five controversial topics in a row (Mark 2), and Jesus decides to tackle generational curse first.
In Mark 2:1-12, Jesus is in the town of Capernaum, and there's a huge crowd forming around him. His popularity is so big that a lot of people are having a tough time getting near Jesus. Four men wanted to bring their paralytic friend to Him, but they couldn't because of the chaos (Jesus was in a building). The men dug a hole in the roof of the building and lowered their paralytic friend on a mat into Jesus' presence.
When Jesus saw the man, His first response was, "Son, your sins are forgiven" (2:5). The religious rulers in the building gets angry and says, "Why does Jesus talk like this? He's blaspheming! Who can forgive sins but God alone?" Long story short, Jesus rebukes the religious rulers and then tells the friend to get up. He gets up and goes home praising God.
Why doesn't Jesus just heal the man? Why does He "forgive his sins" first? To understand what is fully going on here, we have to know the context.
The Jewish civilization based their lives around the narratives found in the Old Testament. In the book of Exodus, God gives Moses a list of Laws for the Jews to live by. After receiving the Commandments, God has a chat with Moses. In this conversation, God reveals His character. He calls himself "the compassionate and gracious God, slow to anger, abounding in love and faithfulness, maintaining love to thousands, and forgiving wickedness, rebellion and sin." Then, he says, "Yet he does not leave the guilty unpunished; he punishes the children and their children for the sin of the parents to the third and fourth generation.” (Exodus 34:7-8)
A little later in the Bible, we come across Deuteronomy 28:15-69. The people are nearing the end of their 40-year journey to the Promised Land and Moses gives them a recap of the Laws. At the end of the speech, he gives a long list of blessings that come with obeying God's word, then follows it with a longer list of "if you don't do as I say, bad things will come to you" things.
These verses were meant to point at a bigger truth about raising your family according to godly wisdom. The warnings found in these two sections of the Old Testament were meant to encouraged them to raise their kids in the way of the Lord. What they weren't meant to do, was to adapt these passages into world views in which to judge others. Today, scholars call this the deutero-historic lens.
This means (very simplistically), if you do something good, God will reward you with blessings. If you do something bad, God will curse you. This is good wisdom - do good things, not bad things. This principle was never meant to be our primary lens, by which we view the people around us.
So, when a paralytic man was brought to Jesus, the thought that was going through the minds of the religious people were, "I bet his grandfather did something really bad!" or worse, "What terrible sin did you commit?" To sum up their thoughts, they would have silently accused the paralytic man in unison, "God hates you" or "God has turned His back on you."
When Jesus said, "Your sins are forgiven," He wasn't announcing that the man was guilty of doing something that led him into paralysis, and that Jesus forgave him of that specific sin. Instead, He was making a statement. "Child, God does not hate you. What you are experiencing is not a result of the sins of your grandparents." The implication of this message is heavy for the religious leaders. It means that their blessings (wealth, notoriety, luxury, etc.) was not a sign of them being favored by God. This is why they were so angry at Jesus.
In essence, Jesus was saying that this broken (and sinful) world has brought diseases and disabilities upon the people of this world. No one is to blame for this man's misfortune. But God is in this house, and He is here to make all things new.
In case you were wondering, Jesus' denial of the deutero-historic lens is not a new idea. If you carefully read through the Old Testament, you'll find passages that challenges this worldview.
For example, there's a book called Job where bad things happen to a good and faithful man. Throughout this narrative, Job's friends keep telling their broken neighbor that he must have done something wrong, to which he cannot agree.
Another book in the Bible, Jonah shows God showing favor towards Nineveh - the bully world-power of his day. Jonah wants God to curse them, but instead, He shows mercy and grace to them. Wait- what happened to cursing their decedents to the third and fourth generation?
The big verse that pushes back on the generational curse is Leviticus 25. Every fifty years, God gives His people a big do-over. If our lives were a big etch-a-sketch, this is God's way of shaking the toy so you can start on a new canvas. Your misfortunes will not get passed onto your children. This is great news to those who made a mess of their lives, but not so good for those who were successful.
The verses in Exodus and Deuteronomy seems to point at the fact that there are some things we do today that have long-lasting effects (to our children and on). But, Jesus declared that these generational consequences does not imply God's hatred toward you or your children. Furthermore, He demonstrated through His death and resurrection that He is interested in making all things new (healing, breaking bondages, restoring relationships, etc.).