The skin is our largest organ, it comprises three layers (the epidermis, dermis and hypodermis), with the epidermis forming the very outer layer between us and the external world. The epidermis itself has an outer layer (the stratum corneum) which forms a physical barrier to chemical irritants and prevents water loss in to the atmosphere. It is important to understand how these elements of a baby's skin differ from an adults, as it is these which are affected by the use of massage oils.
For a baby born at term ie after 38 weeks of pregnancy, the skin is mature enough to function sufficiently outside of the womb, but until about 12 months of age the stratum corneum and the epidermal layer are significantly thinner than an adult's. In the first six weeks or so, the stratum corneum is at least 30% thinner and the epidermis 20% thinner. This relatively thin protective barrier, coupled with the fact that a baby's surface area to body weight ratio is significantly larger than an adults, means that there is a higher permeability through the skin in both directions. Water loss (on the outbound) resulting in potentially drier and more easily torn skin; plus chemicals and irritants (on the inbound) present a greater risk of infection and chemical absorption in to the bloodstream. All of these in combination can have ongoing effects on the development of the epidermal layer itself.
Dermatologically speaking, all massage oils advocated for use on babies not created equally due to their chemically-active contents having different effects. The risks and benefits of using various types of oils is a topic that all baby massage courses should cover in sufficient detail, so that parents can make an informed choice about what they use when massaging their babies at home.