Why is oil the suitable "matter" for the Sacrament of Confirmation? The Catholic Church teaches that for each of the seven sacraments she administers, there is matter and form of the sacrament [cf. Sacraments | New Advent].

Some catechisms also describe a sacrament as "an outward sign of inward grace instituted by Christ".

To me, it is easier to understand "pouring of/living water" being the matter of the sacrament of baptism [cleansing from original sin], but it is not readily apparent to me why anointing with chrism is required matter for the sacrament of confirmation.

Why is oil the suitable matter for the sacrament of confirmation?

The best answer will also explain how oil is connected with receiving the Holy Spirit in the sacrament of confirmation.
Both the new and the old Catechisms have something to say in this respect, and approach the subject from slightly different angles.
The Roman Catechism states in its article on Confirmation:

We now come to treat of the component parts of the Sacrament, and first of its matter. This is called chrism, a word ... appropriated by common usage among ecclesiastical writers to signify that ointment only which is composed of oil and balsam with the solemn consecration of the Bishop. A mixture of two material things, therefore, furnishes the matter of Confirmation; and this mixture of different things not only declares the manifold grace of the Holy Ghost given to those who are confirmed but also sufficiently shows the excellence of the Sacrament itself.
... Nor indeed could any other matter than that of chrism seem more appropriate to declare the effects of this Sacrament. Oil, by its nature rich, unctuous and fluid, expresses the fullness of grace, which, through the Holy Ghost, overflows and is poured into others from Christ the head, like the ointment that ran down upon the beard of Aaron, to the skirt of his garment; for God anointed him with the oil of gladness, above his fellows, and of his fullness we all have received.
Balsam, the odour of which is most pleasant, can signify nought save that the faithful, when made perfect by the grace of Confirmation, diffuse around them such a sweet odour of all virtues, that they may say with the Apostle: We are unto God the good odour of Christ [cf 2 Corinthians 2:15]. Balsam has also the power of preserving from corruption whatever it is used to anoint. This property seems admirably suited to express the virtue of the Sacrament, since it is quite evident that the souls of the faithful, prepared by the heavenly grace of Confirmation, are easily protected from the contagion of sins.

Chrism is still formulated of (usually olive) oil and balsam. The website ForYourMarriage.org, created and maintained by the U.S. Conference of Catholic Bishops, states in an article on it:

Like all our sacred oils, Chrism is made from olive oil, although other vegetable oils can be used if olive oil is unavailable. And like the other two, Chrism is blessed at the end of Lent by the diocesan bishop, at a special liturgy called the Chrism Mass.  Unlike to other sacramental oils. Chrism is scented, usually with essential oil of Balsam, giving it a woody, pine-like fragrance.

The current Catechism has a slightly different take to the reasons for chrism's suitability:

Anointing, in Biblical and other ancient symbolism, is rich in meaning: oil is a sign of abundance and joy; it cleanses (anointing before and after a bath) and limbers (the anointing of athletes and wrestlers); oil is a sign of healing, since it is soothing to bruises and wounds; and it makes radiant with beauty, health, and strength.
Anointing with oil has all these meanings in the sacramental life. The pre-baptismal anointing with the oil of catechumens signifies cleansing and strengthening; the anointing of the sick expresses healing and comfort. The post-baptismal anointing with sacred chrism in Confirmation and ordination is the sign of consecration. By Confirmation Christians, that is, those who are anointed, share more completely in the mission of Jesus Christ and the fullness of the Holy Spirit with which he is filled, so that their lives may give off &quot;the aroma of Christ&quot;.
By this anointing the confirmand receives the &quot;mark,&quot; the seal of the Holy Spirit. A seal is a symbol of a person, a sign of personal authority, or ownership of an object. Hence soldiers were marked with their leader’s seal and slaves with their master’s. A seal authenticates a juridical act or document and occasionally makes it secret.
Christ himself declared that he was marked with his Father’s seal. Christians are also marked with a seal: &quot;It is God who establishes us with you in Christ and has commissioned us; he has put his seal on us and given us his Spirit in our hearts as a guarantee&quot; This seal of the Holy Spirit marks our total belonging to Christ, our enrollment in his service for ever, as well as the promise of divine protection in the great eschatological trial.

(Catechism of the Catholic Church, paragraphs 1293–96)
In summary, then, one can say that the oil of chrism, when used for Confirmation, has the following characteristics:

By its fluidity, it signifies grace flowing from Christ to the confirmand.
By its smell, it signifies the diffusion of the virtues of Christ around the confirmand.
By its historical associations, it signifies being set apart for God, sealed by the Holy Spirit, marked as belonging to God.

These are the reasons why the Church believes the oil of chrism to be the appropriate matter for the Sacrament of Confirmation.