I am a veteran of a thousand such discussions. Run! They always end in flames 
But if youâre like me and canât resist:
Well, it should have such a system if the players want to make the social interaction of the characters part of the âgame,â if the players want their characters to throw them curveballs that they have to roll with, rather than being in complete control of the characterâs internal reactions. Burning Wheel social mechanics force change on characters and demand that a player accept that the system will sometimes constrain their behavior. If that seems like an exciting challenge to the players, then such a mechanic is a good fit for them.
What are itâs advantages?
Well, it allows you to engage the system during some of the most dramatic and intense moments in a session, when youâre roleplaying your character interacting with other characters. To me thatâs a strong advantage, but if someone wants a free hand to roleplay things as they see fit, they will likely see it as a disadvantage.
Why is it sometimes good to loose control over a character?
Because it is another avenue for surprise and challenge during play.
Why donât you want to game without one?
That may be making too strong a point. I play games without social resolution. But, I will say that my favorite games all include it in some measure. And I prefer them for the reasons above.