No, this isn't normal. A little flaking, perhaps, when you go over 600°F, but 500°F shouldn't do anything. It shouldn't even smoke.
Something is wrong with the seasoning on your pan. From the fact that its smoking, I'd guess its not sufficiently baked on. Alternatively, maybe the pan wasn't clean when you applied it.
If its just not baked on, I'd remove all the flaking bits (with some harsh scrubbing, sand paper even), clean it thoroughly, then bring it to around 300°F (stovetop or oven). This will make sure it is completely dry. Spread a thin layer of high-iodine value oil (flax seed is great, soy is pretty good and cheap and easy to find: look for the bottle that just says vegetable oil and check the ingredients, it's probably soy). Spreading is easy with a paper towel.
Next, toss into a very hot oven, 400–500, smoking is expected. Bake for 90 minutes, then turn the oven off. Allow pan to cool with oven. Once its cool, touch it. If its at all tacky, put it back in the oven, and bake for another hour (once again, allowing to cool with oven). It should be a shiny black at this point, and not at all tacky.
You can repeat the process to add more layers. Two should be reasonably non-stick to start cooking on.
If it still peels off after this, you're probably going to need to strip the seasoning and re-season the pan, after stripping it to bare metal. See What's the best way to season a cast iron skillet? to season it from bare metal.
If all the seasoning is completely removed, it will look shiny like brushed or polished metal. This takes a lot of time, and often power tools. I would first ask whether this is what you want to do: does the pan feel waxy, and have a surface that turns glossy when heated? Then there is wax which can be easily removed with a scrub-brush while water is boiling in the pan. Finish with a little soap and hot water, and you're ready to season.
If it is, in fact, the seasoning you want to remove (if, for example, it is coming off in places, or parts are rusting, typically on cookware which has been left outside), the easiest procedure is to heat the pan very hot, either in the coals of a campfire, or in an oven on 'clean' to burn off the previous coating (don't do this with a pan coated in wax, the wax will burn and smoke), then brush with steel wool until the metal pan starts to show through. You will need to season with several coats of an oil like crisco or coconut, and this will take a lot of time. It's rarely necessary to strip a pan unless it is in awful condition.
At the point you're at, I'd assume that any wax or residue is gone from your work with the steel wool, and that you don't need to go as far as to strip the whole thing. To salvage it, put aside the steel wool, scrub with a plastic brush and hot water until the black residue is gone. Clean a little more using a rag and oil (which will pick up oil-soluble debris) until that is clear. Then season as you normally would, using a light oil like crisco in the oven.
Best Answer
I strongly advise against doing it. I tried stovetop seasoning at home and got terrible results.
A stove gives you hot spots - on gas, this will be the ring where the flame touches the metal. The temperature of the metal in this hot spot is way too high, and the oil burns instead of polymerizing. You get some oil-charcoal in this place, which doesn't have non-stick properties, and flakes off after a few uses.
Outside of the hot spots, the temperature is not high enough. The oil doesn't polymerize thoroughly, and forms a sticky paste instead of a smooth one. Your food will stick to these parts of the pan even worse than to the charcoaled parts.
Conclusion: use an oven. If your oven is too small for a pan (I only have a toaster oven, 30x30 cm, and my pan+handle is way too long even for the diagonal), leave the door cracked and seal the crack with alu foil. This is not very energy efficient, but you only do it once per pan. It worked for me, and I got a real, non-stick seasoning after multiple failures on stovetop.