Dear Israel,

look at it from a molecular basis: How can you oxidize proteins, DNA and lipids? Lipids differ prom proteins and DNA by having isolated or conjugated double bonds, while DNA and proteins contain aromatic rings.

The double bonds in fatty acids easily react with oxygen, as you can smell from aged oils and fats. For aromatic rings, you need more drastic conditions, have a look e.g. at the (now mostly obsolete) industrial synthesis of maleic anhydride from benzene by oxidation with air.

The interior of cells is reducing environment. Lipids (and thus fatty acids) are present in the cell membrane, so their chance to have contact with oxygen from the blood stream or from air (lungs, skin) is much higher.