Let's start with the basics that have already been pointed out. A lens with an f/1.2 maximum aperture needs to be (at least) one and a half times larger in diameter than a lens with an f/1.8 maximum aperture. 1.5 times the diameter (and thickness, of course) means 2.25 times the area and 3.375 times the volume of glass. And that means that you can expect to pay about three and a half times as much if the designs are otherwise identical. They aren't.
Lens elements that are composed of spherical curves are relatively easy to grind and polish. I say "relatively easy", but getting the kind of precision required for focusing light cleanly still takes a bit of doing. The shape must be perfectly radially symmetrical, or the lens will exhibit astigmatism (that's where lines at different angles will focus at different distances). If the curve deviates sagittally—if the cross-sectional shape of the lens is off—you'll get coma (a smearing of the image outward from the centre). The larger the lens element, the more precise the grinding and polishing have to be to avoid astigmatism and coma.
Lenses can be thought of as prisms with a continuous curve. If there were only one element, even if that element is made of the finest and most advanced optical glass ever formulated, you would get a tremendous amount of lateral and longitudinal chromatic aberration. That's essentially a prism doing what prisms do: the bend different wavelengths of light by slightly different amounts, producing the familiar rainbow spectrum. The larger a lens is, the more difference there will be in the angle of incidence of the light at the centre of the lens and the light at the edges, and the worse the chromatic aberration will be.
While a spherical shape is easy to produce (either convex or concave), spherical lenses (and mirrors) can't focus light from all points of the lens in the same place. That's called spherical aberration, and it results in a blurry image. Again, the larger the lens, the worse the problem gets. A very, very tiny (slow) lens can get away with being spherical without much penalty; a large (fast) lens will be terminally soft without major correction.
Most of the problems with real-world lenses come from the lens having a large diameter. There are ways of correcting the problems (like using convex/concave pairs of elements to undo the rainbow problem, aspherical—and much harder to grind and polish—elements to reduce or eliminate spherical aberration, using exotic glasses and crystals to minimize chromatic dispersion, and so on), but the larger the diameter of the lens, the more needs to go into correcting the problems. If an f/1.2 lens had the same design as the f/1.8 lens, either the 1.2 would be terminally soft with heavy colour fringing, or the 1.8 would be overdesigned to a ridiculous degree and outrageously costly.
That's just the optics. Now take into consideration that if you want the f/1.2 lens to focus on the same day that you pressed the shutter button halfway, with glass that is going to weigh at least three and a half times as much, you're going to need a stronger focus motor, and the focusing mechanism (the helicoids and gears and so on) needs to be much stronger to cope with the additional force required.
And now that we've gotten to the point that the lens is going to be considerably more expensive anyway, it's time to consider what people are going to expect from an investment of that magnitude. It's one thing to have to buy a $120 lens every few years if you have to; it's quite another to have to pop for a lens that's going to cost, say, a thousand dollars anyway (if only the minimum optical and mechanical upgrades are done). The build quality of the lens isn't just a luxury—no pro is going to invest in something that is both expensive and disposable, so the lens needs to be built more solidly and with a bit more safety factor in the engineering. Add in features that working pros are going to want (like weather sealing) and the cost rises again, but not as much as those things that are necessary just to make an f/1.2 lens work well. And there's one last thing to take into account: when you make expensive things, you don't get as many people buying them, so you lose the economies of scale.
So whether it's the red ring on a Canon "L" lens, or the equivalent gold ring on a Nikon, you're not just paying for a racing stripe and bragging rights. If you don't need the lens, don't buy it. If you do need the lens, though, you're not being charged an "idiot tax"—they actually are a lot more expensive to produce and distribute.