The only reasoning I can think that Spurrier would quit mid-season is that South Carolina already knows who their next head coach is going to be(maybe an assistant that is already on staff?) and he wanted to give that guy a leg-up on holding onto recruits for next year, rather than letting rumors circulate for the next couple months that he was going to leave. Someone had(or was going to) leak the info right now, I bet, so Spurrier just went with it rather than trying to cover it up until the end of the season only for it to eventually be true.
That's the only scenario I can think of that makes sense. He doesn't seem like the type that would just randomly bail mid-season for no reason.