Why do so many preachers pray over people by saying "I break all generational curses on you"?
I read what you wrote about God visiting the iniquities of the fathers on their children, but I still need biblical verses to disprove these preachers and convince myself.
"For the time will come when they will not endure sound doctrine, but according to their own desires, because they have itching ears, they will heap up for themselves teachers; and they will turn their ears away from the truth, and be turned aside to fables" (II Timothy 4:3-4).
I don't believe this statement is popular in my part of the world, but then the belief in curses is not as prevalent here either. You will find false teachers who will tell people anything they want or expect to hear in order to gain followings.
The claim is that God curses a family because of an ancestor's sins and the descendants are being punished. I demonstrated in "Can you explain what it means that the sins of the fathers are put on the children?" that this isn't what God meant by the phrase "The fathers have eaten sour grapes, and the children's teeth are set on edge" (Ezekiel 18:4). It is what people claimed was happening, but God said that He would (and did) show in Ezekiel 18 that people are punished for their own sins, not because their ancestors sinned.
God has pronounced curses because of people's sins. We all suffer because of Adam and Eve's sin. Women have labor in child bearing and men have to work to earn a living. But in part, we suffer from Adam's sin because we continue sinning. "Therefore, just as through one man sin entered the world, and death through sin, and thus death spread to all men, because all sinned" (Romans 5:12). God, through Noah, cursed the descendants of Canaan. It started with Ham's sin, but we later learn that the Canaanites had gone from bad to worse over the years. The reason why a parent chooses to sin is too often taught to their descendants.
But think a moment what these preachers are saying. Men might curse someone else, but they don't really have the power to bring it about, especially after their own deaths. The only curses that have power behind them are those pronounced by God. These preachers are saying that they, as individual human beings, are stopping what they claim God set to happen. If they claim it isn't really them, but God doing it through them, then they are claiming that God is going up against God. God doesn't bow to the whims of men and He isn't inconsistent as these preachers imply.
I did a search of the Bible and there is no mention of breaking curses that I can find. Thus, they are claiming to do something that the Bible doesn't even teach.