What is the ruling on one who considers it lawful to curse their children, arguing that they are their children, and does this constitute an act of disbelief (kufr)?

The questioner seems to be overly scrupulous or obsessive regarding issues of disbelief (kufr). We advise him to be gentle with himself and not to delve deeply into this matter. For one whose Islam is established with certainty, it is not removed by doubt. An individual is not declared a disbeliever unless the conditions for declaring someone a disbeliever are met and there are no impediments to it. As for a father cursing his son, it is permissible as long as it does not involve invoking a curse or slandering him.