The real reason probably has something to do with what happened back when Yuma and Jun first met.
It's explained in Jun's story in Re:Lucks. They met when they were children. Yuma told Jun that he looked too pretty to be a boy. Yuma also told Jun that he thought it was cute when Jun refered to himself as "atashi" (exclusively female version of "watashi" [word used for refering to oneself]). Jun secretly fell in love with Yuma at the time, and has been acting like a girl ever since.
It's a real travesty that Jun's voice actress was changed for the anime. Even bigger travesty that Jun refered to himself as "watashi" in the anime...
The first-run of Happiness! for PS2 is going to include a special anime DVD that explains Jun's origin. I'm guessing that it's just going to go into depth of what has already been revealed in Re:Lucks.
That's good info, but would you care explaining why in the CG gallery in Re:Lucks there are two CGs for each of Jun's scenes, one where s/he has female reproductive organs and one where s/he has male ones?
During the last 1/4th of Jun's story in Re:Lucks, the player is presented with a choice to either : leave him as a boy, or tell him to turn himself into a girl with the use of magic.
It's much more complicated than that, but I don't have the patience to explain everything.