When cooking oil starts to smoke, it means that it's starting to break down. The more it breaks down, the less effective it is as a cooking agent; and the worse it begins to taste. Of special interest to you as you cook for your family, oil which has been overheated has adverse health consequences.
The smoke point itself, is not a magic place where before everything was hunky-dory, but as you hit it all of a sudden tons of bad things start, and the whole world goes to kablooey. Rather, things start to happen as the oil approaches the smoke point, and get worse the farther beyond the smoke point and the longer the higher temperatures are held. It's more accurate to think of the danger zone for oil being a range.
In fact, you can see the oil start to darken before it goes dark. Oil which has been reused several times will start to darken even if it's kept within the safe temperature range, and this is a sign the oil is breaking down into its components of fats, water, and "other stuff" (chemical term). Darkening and smoking are both signs of separation and degradation -- and result from the action of heat on the fats (lipids, lipoproteins).
There are assorted health dangers associated both with the fumes and the oil. The oil and food cooked in it is bad enough, but the fumes are particularly bad for you. They are supposedly quite carcinogenic, and an otherwise healthy diet is not a remedy.
Some restaurant kitchens use the smoke point as short hand for "NOW." A small amount of oil in a very hot pan over a very high flame will hit the SP pretty quickly, and getting the food in right away will reduce the heat to where things won't taste bad -- and most of the bad stuff hasn't happened anyway. But restaurant kitchens use flame you can't get on a residential stove and work at a level of timing and teamwork you can't imagine until you've done it. This is one of several restaurant practices you shouldn't imitate.
Even though it's ingrained in a lot of restaurant kitchens, it's bad technique. Better restaurants encourage cooks to start just below the smoke point and not use the SP as a reference. You don't live in a restaurant, and the smoke point is something you should experience only by accident. If you smoke the oil, throw it out and start over.
If you're using a small amount of oil, as for a saute or a sear, preheat the pan empty over your best guess as to what it will be when you cook -- usually medium high -- for about two minutes. Remove the pan from the flame, and while you're holding it off the flame add your oil (this keeps the oil from smoking right off the bat), swirl the oil in the pan (if it's hot the oil will run like water, if it runs slow it's going to need some more heat), and return the pan to the fire. Make sure the entire bottom of the pan is covered before checking for shimmer. If the air right above the oil looks like it's shimmering, the oil is hot and you may add the food. (The shimmer point for everything but butter is about 20 degF below the smoke point.)
If you're using a low smoke point fat like butter or extra virgin olive oil, reduce the heat to medium. Butter will smell like hazel nuts before it starts getting bitter -- that's because the milk solids toast before they burn.
Remember, if anything starts to smell bad -- toss it. It's not worth fooling around with it -- especially in your situation.
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