This video has gone around the internet for probably ten years now. If you've seen it before, the video won't be as powerful, but you know what I'll be describing. If you haven't, watch it. I'll wait.
*whistles and pauses*
Done? If you are astonished how you could miss something as obvious as that, then let me introduce you to change blindness, and the larger phenomenon of inattentional blindness. Simply, both of these are the inability to detect changes in your visual field due to significant attention being placed on a task already. This makes sense, as if you were to react to every single thing in the environment, you wouldn't function—change blindness is adaptive. But the adaptive nature starts to break down when you pay attention to the wrong thing (a cellphone, perhaps?).
The above video is very good because they take advantage (possibly inadvertently) of research done on multiple object tracking. Research has found that we are pretty accurate at tracking the location of multiple objects at once (we're 85% accurate with 5 items), but the more things we keep track of, the less details we can distinguish about the world around us, and the things we are keeping track of. This means that, since we're actively keeping track of the four players in white and the ball, while also keeping track of the players in black with the ball to do differentiation, we have no awareness of the bear coming into the frame—we just don't have the capacity to track it.
I hear someone saying (or at least preparing to type), "Sure, then that means I'm pretty good at making sure there's a car ahead of me, right?" Tell me a situation on the road where you're only tracking four objects, and have room to track your phone too. Also, remember the change of details? If you have just began to track that light coming into your field of view, you are unlikely to notice it suddenly change from yellow to red. Even if, in most scenarios, the way lanes are set up limit the possibilities with your field of view, nothing is changing the fact that you are taxed with visual stimuli in the world. Why would you want to take the risk in adding a distraction? Why would you take up your cognitive resources to track an e-mail that can wait until later? Torch is definitely right in explaining why you only need to drive, but I hope I've explained well the psychological reasons why it is prudent to do so too.
I am a Psychology/Cognitive Science student, and I like trying to apply what I learn to the real world. Mostly, I'm a big nerd.