The width of a tire is not an issue, as was already said. If anything, wider is better. The wider contact patch means better traction, more stability, and a better chance of keeping yourself from getting stuck in ruts from that extra width.
The reason mx racers will run the smaller 18" rears is because they weigh less, and have a lower tire profile, which gives a sharper response in corners. The low profile sidewall also makes it a lot easier to accidentally unseat the bead, which is why most racers will run beadlocks.
Small tires like these are only good for racing on tracks. If you try running these smaller tires in the woods you'll probably have issues. The smaller sidewall can cause a lot of problems, aside from being easier to knock off the bead, it's also going to make your wheels much more prone to damage from rocks, and it's a lot more likely that a sharp impact will pinch the sidewall of the tire and cut it, because there's not as much tire to absorb that shock. Ground clearance is another big issue, an 18" tire kills ground clearance and that's a big issue for most trail riders especially in rutted and muddy areas. And although it's not directly related to the size, 18" and 19" tires are designed for mx, and in the pursuit of shaving off a few pounds, most of these tires are 2 ply which is usually not durable enough to withstand much abuse in the rough terrains.