Being he is going to Ohio State I can't imagine he was pushed out, it's technically a big promotion for him going to a program with the history that OSU has even with all their pending sanctions.
The last guy who held the position at Ohio State is referred to here as "the video editor".
Ohio State Hires Tom Herman
QB coach is not a promotion. Certainly not a "big" one. I'm sure he wants it for whatever reason, but straight line promotion? No way. Maybe it frees up his future prospects, but it is like going from the executive suite to the staff of another company in hopes that someday the hiring company will promote you to CEO, or you'll get noticed and stolen by a prestigious company for a better job.
But making the move from Offensive Coordinator to upgraded "video editor" (in OSU fans' words) is not a promotion.
Don't get me wrong - QB coach is critical and instrumental, but OC's don't get "promoted" to that position. The proper term is "reassigned."
Best case scenario, he's reshuffling his career to take a launch at a Head Coaching gig. Worst case? He goofed up. Also possible: force-out.
I honestly couldn't tell you which of the three is more likely. All of it is vague.