Objection 1. It would seem that the whole body should be anointed in this sacrament. For, according to Augustine (De Trin. vi, 6), "the whole soul is in every part of the body." Now this sacrament is given chiefly in order to heal the soul. Therefore the whole body ought to be anointed.
Objection 2. Further, the remedy should be applied to the part affected by the disease. But sometimes the disease is general, and affects the whole body, as a fever does. Therefore the whole body should be anointed.
Objection 3. Further, in Baptism the whole body is dipped under the water. Therefore in this sacrament the whole body should be anointed.
On the contrary, stands the rite observed throughout the Church, according to which in this sacrament the sick man is anointed, only in certain fixed parts of the body.
I answer that, This sacrament is shown to us under the form of a healing. Now bodily healing has to be effected, by applying the remedy, not to the whole body, but to those parts where the root of the disease is seated. Consequently the sacramental unction also ought to be applied to those parts only in which the spiritual sickness is rooted.
Reply to Objection 1. Although the whole soul is, as to its essence, in each part of the body, it is not as to its powers which are the roots of sinful acts. Hence certain fixed parts have to be anointed, those, namely, in which powers have their being.
Reply to Objection 2. The remedy is not always applied to the part affected by the disease, but, with greater reason, to the part where the root of the disease is seated.
Reply to Objection 3. Baptism is given under the form of washing: and a bodily washing cleanses only the part to which it is applied; for this reason Baptism is applied to the whole body. It is different with Extreme Unction for the reason given above.
Source: Summa Theologica (New Advent)