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If you look at a tire from the rear, you'll notice that the tire isn't quite a cylinder. It has edges that are slightly beveled. Sometimes this effect is clearly apparent, but other times, as in many car tires, it's hard to see.
I can understand the use on motorcycles, since they are typically angled on turns, but cars are, in general, not designed to take corners on two wheels.
Why do cars have beveled tires?
When a car turns the sideways force will pull the outer side under the rim. A angle sticking out will get worn off quite quickly.
Also if a tire isn't properly inflated then the walls will bulge over and put more force on the outer side. Again a corner will get worn off rapidly under these circumstances.
To add to @ratchetfreak's answer, there 2 more reasons:
1. Manufacturing process It's much easier and more reliable to make a continuous surface that us bevelled, that an angled surface from rubber material.
2. Stress distribution For the same reason why airplane windows are rounded, car tires are beveled. Stress is much better distributed when surface s continuous. By introducing angles, you would concentrate stress in those areas leading to premature failure.
If you press a cylinder on a flat surface the contact pressure concentrates on the edges and becomes very high. We call that edge stress condition. If the cylinder has a profile (curved instead of straight) it causes the pressure distribution to be more even and hence lower in value.
If you want to account for the slight angles at which tires approach the road and not cause the tire to roll on one edge only you need a profile.
Some roads are not convex, but rather concave, and a flat cylinder would not roll well with the edges in contact only.
In fact, the restoring moment (response torque to slip) is proportional to the width of the contact patch, and when edge loading occurs it throws off the handling of the car. Ever try to steer a car with a deflated tire? It is very hard to do.
