They call it the "dark side" for a reason.
A while back, Kate discussed the perils and pitfalls of using a car tire on the back of your motorcycle, a practice known as "the dark side." A video just came across a Facebook group I'm on demonstrating, clear as day (the daylight you actually see under the tread), why this isn't good.
What it comes down to is simple. Bikes lean. Cars don't. OK, yes, cars do lean a little due to weight transfer and suspension loading and unloading. I autocrossed for years—I get it. In the car world, though, we fight against this lean as much as we can with stiffer springs and sway bars. We'll even dial some negative camber into the alignment so that when the car goes around a corner at full tilt, the tire is straight up and down for maximum grip. A car tire has its maximum grip when its full tread width is in contact with the road.
Motorcycles, on the other hand, need to lean in order to turn at any speed faster than walking. It's the fundamental way that bikes work. Motorcycle tires are made to lean. Their profile is round, not square like a car tire. In most cases, you're either going to drag hard parts while leaning hard or chicken out before you lean hard enough to get onto the tire's sidewall.
Here, though, we have a perfect view of a car tire on the back of a Honda Valkyrie. On the surface this may seem like a good idea for such a big, heavy bike, especially if it does a lot of highway travel where it doesn't lean much. Here, though, it's on the Tail of the Dragon, a stretch of US 129 on the border of North Carolina and Tennessee with 318 curves in just 11 miles. It's a twisty paradise for motorcyclists and sports car drivers, but the worst-case scenario for a car tire on a motorcycle.
I encourage you to watch the video, but even the thumbnail says it all. When the bike is leaned over, that car tire is on its edge, with only about one-third of the tread contacting the road. This is the exact situation that autocrossers strive to avoid. Even worse, the harder you turn, the more you lean, and the less tread contacts the road precisely when you need grip the most. In particularly hard turns, the car tire rolls up onto the sidewall, which is never intended to contact the road. I've had road debris puncture tires on my cars without much difficulty. You don't want to vastly increase the chance of this happening by placing the sidewalls directly on the road.
If the only riding you do is long stretches of highway with no turning at all, I suppose a car tire could work. They do last much longer than motorcycle tires, though if you're leaning hard through the turns the edges of the tread will wear extremely quickly. Ask this former autocrosser how I know. Personally, I find the turns to be the most fun and challenging part of riding. If I'm going to attack the twisties, I want a back tire that's designed for the job, and that won't give up its grip right when I need it most.