This is definitely something that caught me off guard.  The way I see it, one of three things happened.
1-The Bears knew they wanted Babich to assume the DC position all along and didn't announce anything so as not to submarine Rivera's chances at a HC position.  Analysis: this would be a class move and, assuming Babich justifies their interest, a nice pre-emptive move to keep things fresh.  It's Lovie's defense after all, right?  Likelihood: I'm not sure on this.  I did see some smoke before the off-season about the Bears promoting Babich if Rivera left.  Maybe those stories were planted?  Maybe that's why Johnson was curiously let go.  I guess if you're into conspiracy theories, you and Oliver Stone would deem this to be the backstory.
2-Rivera knew he wanted out and had told the Bears as much.  Knowing that the only possibility was a remote one that would involve paying out the nose to retain Rivera's interest, the Bears let him go and turned their attention to Babich.  Analysis: If this was the case, you can't really fault the Bears.  Depending on the details, it wouldn't exactly be cool for Rivera to hang his former employer out to dry.  Likelihood: I'd say low.  I just don't see why taking a demotion would entice Rivera sooo much.  We can argue about gaining experience, but the fact is that just about every team that runs a 3-4 brought in a new coach in the past 2 years (w/ the Pats being the possible exception and I don't see them changing horses).  The league seems to be trending towards a 3-4 right now but I know I wouldn't make a move down b/c of that.  
3-The Bears are cheap and didn't want to pay out the nose for a coach when Lovie really runs the D.  Angelo tells Rivera we'll offer this much and Rivera says he'd much rather look for greener grass.  Analysis: I hate having a penny-pinching team.  The money's there, I know it is.  But I suppose the Pats have done a good job running a budget-conscious organization and I can understand rejecting the Cubs, er Yankees, Fiscalities-be-Damned approach to team-building.  It would suck if this was the case.  Likelihood: Given our history, I'd say high.  However, I imagine this time it's for a different reason.  Why break the bank when Lovie really does run the D?  Can't we just focus Rivera's money on Turner and Toub?  I've always felt those two were more critical given the Lovie's skillset.  Going into the off-season, my wishlist was as follows: A- franchise Briggs (not necessarily re-sign him), B- Re-sign Ron and Toub.  
In the end, I'm not sure this really hurts our team.  No doubt Rivera's talented and now doubt he had a bigger impact on Lovie's D than he sometimes gets credit for.  However, I'm willing to give Babich a go.  Hell, the Linebackers have played great under his watch, so it will be interesting to see what he can do to the defense.  
As for Rivera, I like the guy but, sheesh.  I really hope this is not a decision he made of his own free volition.  Yes, San Diego is talented.  Yes, the have a lot of toys on defense to play w/ (most notably, steroids).  And, yes, getting 3-4 experience will be helpful.  However, it is a move backwards.  Any way you slice it, that's not good.  Also, Norv Turner is the new coach of the Chargers!!!!!!!  I can not stress the importance of this enough.  Norv=Coordinator.  He's been abysmal at every HC position he's taken.  I just don't see that team doing anything other than regressing.  It's a shame that AJ Smith didn't do the ballsy thing and just hire Rivera or some other guy to shake things up.  I get the feeling the Smith is a little too heavy-handed out there.  

i hope this doesn't lead toless blitzing.

It seems most here would prefer that this breakup be due to a philosophical dispute rather than a contract one.  But while I'm just as opposed to letting Rivera go for financial reasons (there's no salary cap for assistant coaches, and therefore no reason for a major city's team with tremendous resources that just went to a SB to be skimping on   any assistant coach's salary), I'm not sure I would agree with the seeming board consensus that this D is really all Lovie's making, and Rivera's input was either peripheral or harmful.

I know its unclear to us exactly who deserves credit/blame for what in the Bear's defense this year.  But from what I've read, Rivera was the guy who adjusted from the Cover-2 to blitz more and play more man.  The problem people here have with the Bears D in the Super Bowl, was that they played too much Cover-2.  That would seem to be more attributable to Lovie.  If that's so, many of us might side with Rivera in their 'philosophical disagreement.'  

I happen to think that the Cover-2 is a good base defense.  But without some blitzes and man coverage, it gets predictable.  I think the Bears have the corners to play more man, and I like that Rivera did that this year.  I like Lovie as coach.  But I'm worried that his fidelity to the cover-2 will outgrow its usefulness.