Okay this a real fantasy for more guys than I thought. Several guys this weekend said they would love to take me into their local bar back home and show me off.
Definitely it is
very common!
i will allow myself to delve in the male psyche, even though - in all honesty - i am not a professional in this field. But from what i have processed and gathered from other men and, after adding my own self-assessment to the analysis, i tend to believe that the fantasy or behavior you've described is based on
pride. Probably it's also some sort of challenging the "peers" in a competitive manner, or, even more likely, a way to show proof of competitional superiority.
In any case it is also a
huge compliment toward the Woman in this scenario as the "logic" goes somewhat like this... The one who intends to show the Woman in question off to other men perceives her as highly attractive - a Woman who will turn heads no question, a Woman all other men will wish to get in touch with, will become jealous of and envious of the one she is with, the man who presents her in that manner.
It does not essentially differ if the guy is a "cuck" or "Stag" husband/BF or a so-called "bull" in this lifestyle. For either it is the pride of being with a Woman assumingly all other men wish to be with (instead of him). For a husband or boyfriend in a solid relationship the idea may be based more on the fact that he is the one who "has landed" the Woman and who has the ability to keep her - he is the one she chose (not any other guy)! For a "bull" the idea may be based more on his sexual prowess which made the Woman choose him specifically (and not another man), but otherwise the "logic" remains about the same.
i'd like to add that it also does not differ essentially if it stops at showing the Woman off or if it later leads to (sexually) sharing her. The only thing that changes is that in the first case the "logic" goes like this: The man (husband/BF or "bull") presents the Woman to other men as the rolemodel partner, "trophy wife" or Woman the other men lust for (but cannot have)! In the latter case the "logic" evolves to: The other man who the Woman is shared with gets to have a taste for once of what the man who shares her is privileged to have and enjoy on a regular basis.
Well, of course there may be other reasons for a man to show off or share the Woman he is connected with - one way or another. But i truly believe that what i've tried to explain here is most probably the most common psycho-social reason for men to show off or share "their" Women.
Because then i am going to miss her much. 
