He gets paid to beat BYU, to out-recruit BYU, and to keep Utah donors and alums happy. So based on that alone you wouldn't/shouldn't expect him to be very pro-BYU, at least certainly not in public. Remember that Bo Schembechler was an Ohio native and an Ohio State grad. He didn't exactly play that up during those years, nor should he have. His job at the time was to beat Ohio State and be gleeful in doing so.
Does it go any deeper than that for Kwhitt? Does he harbor some actual ill will toward BYU? Maybe. But I suppose I couldn't care less. Y'all need some thicker skin.
Edited to add: Kwhitt is no Schembechler, sorry for the inadvertent comparison.