Why it is important to keep your distance (and watch what is going behind you as well)

My reaction to the cars stopping in front of me was delayed, as I was just looking in my mirror, willing to change the lane.

But thanks to that I noticed that the car behind me is too close. If I haven't moved to the left, he would probably end hitting my rear, as he only managed to stop partially side to side with me (then drove a bit further forward).

well)