A parent can brag about their kid(s) and talk and talk about them, but a person does the same thing about themself and they are considered a narcissist.
Depends upon how one goes about doing that. One can say something about themselves that isn't "bragging" but more informational or entertaining if they wanted. Patting oneself on their own back from time to time also isn't that wrong as long as it isn't to many times and done with modesty not gloating.
Actually, parental bragging can grate on other people almost as much as self-promotion. The inconsistency that i find more harmful is parents who constantly criticize and talk down their kids, then brag about those same kids to other people.
If a male human has sex with multiple female partners...he is considered a "stud" If a female human has sex with multiple male partners...she is considered a "whore" Sexual Double Standard much?