So I was thinking, and here it goes...
Im thinking,Barragan is number two, Stark number one, and Halibel number three.
Lets say, Barragan thinks he should be number one, being number two, allows him to think "Someone undeserving is in my place." This is hinted at by him seeking approval from ONLY Stark in a demeaning manner, when he says hes taking charge.
http://www.onemanga.com/Bleach/318.1/12/
http://www.onemanga.com/Bleach/318.1/13/
Starks lazy attitude also supports Barragans perception of Stark, that he is actually less powerful. Plus the common knowledge that those who have nothing to prove, don't. So he keeps to himself, only exerting his power when needed.
Also taking into consideration the simple facts here, when he said hes taking over, he leaned to Stark, not Halibel. The second huge clue was his fraccion:
Bleach Five Pillars Four Corners page 13 | One Manga
Who seems to have a problem with him following Barragan. I believe there is a mistranslation there too. "What're doing going alone with him!?"
Subsitute "along" in and it all seems to make sense.