Hat tip to TrollhattanSaab for this neat video which clearly demonstrates why you should put your better (newer) tires on the rear wheels of your car--to preserve understeer bias.
So what's so important about keeping the car understeering?
Most drivers aren't skilled enough to correct an oversteer condition (you typically need to apply more throttle and countersteer quickly). Getting sideways means you have a higher chance of rollover due to tripping, or side impact. Most drivers will do the wrong thing for oversteer, they will brake, lifting the rear end further and giving away even more traction, making their problem worse.
But in an understeer condition, the instinct to jam on the brakes is the right one, because it gives more grip to the front wheels, which gives them a chance to regain steering ability. And if you must crash, it is much better to crash head-on because that's where you have the most protection from your crumple zones and seatbelts.