One would think that a natural oil like olive oil would be okay for applying to a child’s or adult’s skin? However, you need to be aware that it can potentially be harmful to skin, especially if the skin tends to be dry or if it is already affected by eczema.
Olive oil is low in linoleic acid (a fatty acid) and high in oleic acid (another fatty acid).
Linoleic acid (not to be confused with linolenic acid) is from the Omega-6 fatty acids family, having “anti-inflammatory, acne reductive, and moisture retentive properties when applied topically on the skin” (Wikipedia). You would really be looking to apply oils with higher linoleic acid content, not less.
On the other hand, oleic acid improves the permeability of the skin, meaning water and oil can be absorbed in and released out of the skin easier. This can be a good thing for most people. However, in dry skin or eczema-affected skin that already struggles to retain moisture, this could lead to more water/moisture loss and worsen the skin’s condition.
More reading about olive oil can be found below…
Daily Mail UK “How ‘gentle’ skin creams could give your baby eczema”
Another substance commonly applied to babies’ skin is olive oil — but Professor Cork says this is also unsuitable as it has a very poor balance of oleic and linoleic oil, which is damaging to skin before it develops properly.
The acid-alkali balance in these oils (measured on the pH scale) is not suitable for a baby’s sensitive skin, as it hydrates it for several minutes but then has a drying effect.
Baby Centre UK “Is Olive Oil okay for baby massage?”
http://www.babycentre.co.uk/baby/dailycare/olive-oil-for-baby-massage/
Department of Dermatology University of Connecticut Health Center “Healing fats of the skin: the structural and immunologic roles of the omega-6 and omega-3 fatty acids”
Linoleic acid and alpha-linolenic acid both give rise to other long-chain fatty acid derivatives, including gamma-linolenic acid and arachidonic acid (omega-6 fatty acids) and docosahexaenoic acid and eicosapentaenoic acid (omega-3 fatty acids). These fatty acids are showing promise as safe adjunctive treatments for many skin disorders, including atopic dermatitis, psoriasis, acne vulgaris, systemic lupus erythematosus, nonmelanoma skin cancer, and melanoma.
Eczema 101 