Why is oil used at Confirmation?

This one is a little trickier, because the origins of Confirmation's symbols are many and diverse. One source can be found in the bathing customs of the Roman Empire.

In our times, when you take a shower, you wash up and dry off. Drying off is understood to be part of the total shower. In the same way, the early Church saw Confirmation as a part of the Baptism experience. In Roman times, oil was a part of the bathing "ritual." A bath included both water and oil. The water ritual (Baptism) came to mean the washing away of sin, and the oil ritual (Confirmation) was interpreted to mean the sweet fragrance of God's presence: sanctifying grace.

We know that sin cannot be removed except by grace just as, for example, a vacuum cannot be removed from a container without replacing it (the emptiness) with something. The two go together. In the same way God's grace fills us with redemption and salvation. This grace, this presence of God in us, is the Holy Spirit. Confirmation is the Sacrament of the Holy Spirit.