There is no universal clear reason why some adult children become narcissistic and others don’t. Some theories suggest that genetics are the reason for the development of narcissism, which, like many other personality traits, tends to form in childhood.
There is also the belief that certain family dynamics seem to lead to this personality disorder. The more common thought is it’s the result of living with a narcissistic parent in an absence of love and affection, or being raised in a highly competitive or even shaming environment. Neglect, abuse, or, on the other extreme end, even excessive idolization of a child growing up can play a role.