My Answer:

From a histology point of view:

1. Petro chemicals sit on the skin, not providing real moisturizing and no skin conditioning.
2. Petro chemicals are foreign to the body and therefore can be expected to act as toxins and may bio accumulate.
3. Petro chemicals are known carcinogens when inhaled and ingested. 60-80% of what is applied to the skin is absorbed directly into the bloodstream without the intervention of the liver until these have circulated.
4. Petroleum products have hazards identified with them according to the Environmental Working Group - moderate hazard ratings. For instance, concerns about mineral oil are listed as follows:
This ingredient:
yes, moderate Cancer
no Developmental/reproductive toxicity
no Restrictions & warnings
yes, moderate Allergies/immunotoxicity
no Contamination concerns
no Other moderate concerns for this ingredient:
Organ system toxicity (non-reproductive), Occupational hazards
no Lesser or emerging concerns for this ingredient:
Irritation (skin, eyes, or lungs), Data gaps

http://www.cosmeticsdatabase.com/ingredient/703977/MINERAL_OIL/

I'd vouch for a vegetable oil or wax any day!