I don't think this issue solely pertains to Bitcoin. Who would go on the streets and call out publicly that he or she owns a shit ton of jewelries or valuable watches? Or who would say that they have a bag of money in their basement? I think it is much more basic than saying that claiming to have Bitcoin is dangerous. I would just not brag about my wealth or specific possessions in general.
Bragging any wealth or asset in public specially in social media even if it is not about bitcoin were not necessarily advisable but it's a person's choice if he/she would like to brag his asset. But I believe that no one wants to make it in public because of the possible threat that it may give to a person. However it is undeniable that owning bitcoin could be a good measure that a person has a wealth that they kept in and due to the fact that bitcoin is now known by many and they know the value of this token it is indeed make sense to make it private.