There's no "logic" here, you're just not aware of the history of the term and the sociological history behind it.
The nuclear family was an oddity that developed in England concomitant to the Industrial Revolution in middle-class families for whom occupational relocation was common. It was enshrined as an ideal sociological familial arrangement in the United States because its normalization was conducive for developing larger pools of productive labor.
"Nuclear" here is in reference to households with only mother, father, and children, in distinction to the norm of multigenerational households throughout history and in most of the world today excepting the West.
Did I miss where they claimed absolute perfection in shedding their egotism or something? Because this interpretation of self-reformation after an actually humbling admission of having once lived in devotion to narcissism as being braggartry is what screams insecure egotism to me.
The nuclear family was an oddity that developed in England concomitant to the Industrial Revolution in middle-class families for whom occupational relocation was common. It was enshrined as an ideal sociological familial arrangement in the United States because its normalization was conducive for developing larger pools of productive labor.