Can someone please tell me, why do cooking instructions have you frying in olive oil? That doesn't make any sense as olive oil has a very low smoking point.
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I would suggest three reasons:
- The smoke point of olive oil, while lower than many oils, is higher than most items you would deep fry (375 - 490 F or 190 - 255C, depending on the olive oil).
- Tradition - if it is the oil that is most plentiful, it is the oil that is used.
- Flavor - olive oil imparts a distinct flavor (as other oils do).
If you're sweating, say, a mirepoix, then there is enough energy going into boiling and evaporating the water in the vegetables. The temperature doesn't reach the smoke-point of an olive oil until the water has gone and browning begins, at which point, you start frying. Sweating in olive oil does yield a different base flavor, from other fats.
But even then, I wouldn't use a high-quality, cold-pressed Extra Virgin olive oil for sweating, either. Not because it would reach its smoke-point, but because all the lighter, more volatile fragrances on which its quality depends would be driven off, leaving it 'flat'. Those oils are best appreciated raw.
There are people who are very bothered by eating oil that has been taken to the smoke point. There are those to whom it doesn't matter at all. And there are those who don't even know that this happens.
The first group tries to sell their preference as having universal validity. But in reality, there is no law saying that oil should never be taken to its smoke point. The recipes you have found are written and enjoyed by the second and third group of people.
There are two reasons that come to mind. First, as Chris said, very refined olive oils have a higher smoke point than say extra virgin olive oil and can be used to sweat onions and similar things.
Since you don't specify which recipe, it's also relevant to point out that many recipes are not that good. There is no qualification needed to post recipes on a blog or videos on Instagram or Pintrest. Whoever wrote the recipe might simply not know any better. After all, many popular recipe blogs are run by enthusiastic home cooks, not professional chefs. With the way social media works, styling mediocre food and taking good pictures of it is rewarded more than a good but not photogenic recipe.