I think White's experience here could be explained in couple of reasons:
1) The system he was expected to use was too complicated and was too clunky, leading to mistakes by the entire offense.
2) Being in such a toxic environment for so long made it impossible for him to get out of the funk and regain confidence.
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White got a total change of scenery by going to WKU. Not saying that USF was a bad place for him, but going 2-10, 3-9 under his lead presents a lot of negative stigma. A larger monkey on the back. and if you're a quarterback without confidence in yourself and your team, you get essentially what White looked like for a large portion of his time at USF. He showed flashes of having the arm and the smarts, but (I believe) being so entrenched in the gunk surrounding those good times made it impossible to really rise from the ashes.
Now he's at WKU throwing 5k yards and 40 TDs like its nothing. He was put into a position to succeed, and he's been able to become confident in himself and his throws, and it really shows.