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So, why is flax seed oil singled out?
Using your logic it would seem that it would be worse to cook with Olive Oil (which I do ALL the time) than flax seed.
Note, I got this from a site, but it is accurate so I just copied the parts I deemed important for this discussion.
There are 3 types of fatty acids: 1) Saturates 2) Monounsaturates and 3) Polyunsaturates. The type depends on the number of ‘double bonds’ in themolecule. Polyunsaturates are further divided into Omega-6 polyunsaturates or Omega-3 polyunsaturates. The difference lies in the position of the double bonds in the molecule. Omega-6 fatty acids have the first double bond after the sixth carbon and Omega-3 fatty acids have the first double bond after the third carbon.
The extent of saturation or unsaturation has practical importance for the use of
fats for our health and also in food applications. The more saturated a fat
mixture is, the more likely it is to be solid at room temperature. For example,
lard, butter and palm oil contain mainly saturated fats. However, butter and
palm oil are softer at room temperature compared to lard. This is because butter and palm oil contain a proportion of unsaturated fats mixed with the saturates.
As the proportion of saturated fats decrease and the proportion of unsaturated
fats increase, the melting point of a fat is lowered. Thus, polyunsaturated fats
are liquid at room temperature and generally they remain liquid in the
refrigerator. Monounsaturated fats also are liquid at room temperature, but they begin to solidify in the refrigerator. Saturated fats are solid at room
temperature and in the refrigerator. Fats, which are liquid at room temperature, are called "oils." Because the monounsaturated and polyunsaturated fats are generally liquids at room temperature, they are called oils. Oils can be vegetable, fish, or mammal in origin. Thus, fats derived from olive, canola, sunflower, soybean, cottonseed, and peanut are all oils. In addition, fats derived from fish and seal are also oils. However, some vegetable derived fats are semi-solids at room temperature because they have a significant proportion of saturated fats. Such an example is palm oil.
In addition to being a determinant of melting point, the extent of unsaturation
is also a determinant of the stability of a fatty acid. Instability refers to
the chemical degradation of fatty acids by oxidative breakdown. If all fats were
kept in the refrigerator in the absence of air, they would all be stable to a
similar extent. However, in the real world the methods we use to prepare and
store food, allow the fats to be exposed to oxygen and to heat. The oxygen in
air can react with the double bonds in a fatty acid to initiate its destruction.
This process is increased by heat. In addition to losing the fatty acid in this
process, the by-products of the reaction are free radical compounds, which can initiate chain reactions leading to destruction of other molecules. This leads to unsuitability for consumption. The final result is known as rancidity.
-Oxygen from the air and heat combine to degrade fatty acids
-Saturates and monounsaturates are more stable than polyunsaturates
-The degradation can produce destructive free radicals and off-flavours
-The end-point is rancidity
Therefore, because flax oil has a high amount of Omega-3 fatty acids (a polyunsaturated fat) and olive oil has a high amount of Omega-9 fatty acids (a monounsaturated fat), Flax oil is less stable than Olive oil.
One more note, the more "virgin" the olive oil is, the lower its smoke point (the temperature in which it starts to smoke) and therefore more virgin olive oils are less apporpriate for cooking.
Below are chemical structures of a Saturated (left ), Omega 9 (monounsaturated) (middle), Omega 6 (right) and Omega 3 (bottom left) fatty acids