Objection 1. It seems that the order of the sacraments as given above is unbecoming. For according to the Apostle (1 Corinthians 15:46), "that was... first... which is natural, afterwards that which is spiritual." But man is begotten through Matrimony by a first and natural generation; while in Baptism he is regenerated as by a second and spiritual generation. Therefore Matrimony should precede Baptism.
Objection 2. Further, through the sacrament of order man receives the power of agent in sacramental actions. But the agent precedes his action. Therefore order should precede Baptism and the other sacraments.
Objection 3. Further, the Eucharist is a spiritual food; while Confirmation is compared to growth. But food causes, and consequently precedes, growth. Therefore the Eucharist precedes Confirmation.
Objection 4. Further, Penance prepares man for the Eucharist. But a disposition precedes perfection. Therefore Penance should precede the Eucharist.
Objection 5. Further, that which is nearer the last end comes after other things. But, of all the sacraments, Extreme Unction is nearest to the last end which is Happiness. Therefore it should be placed last among the sacraments.
On the contrary, The order of the sacraments, as given above, is commonly adopted by all.
I answer that, The reason of the order among the sacraments appears from what has been said above (Article 1). For just as unity precedes multitude, so those sacraments which are intended for the perfection of the individual, naturally precede those which are intended for the perfection of the multitude; and consequently the last place among the sacraments is given to order and Matrimony, which are intended for the perfection of the multitude: while Matrimony is placed after order, because it has less participation in the nature of the spiritual life, to which the sacraments are ordained. Moreover, among things ordained to the perfection of the individual, those naturally come first which are ordained directly to the perfection of the spiritual life, and afterwards, those which are ordained thereto indirectly, viz. by removing some supervening accidental cause of harm; such are Penance and Extreme Unction: while, of these, Extreme Unction is naturally placed last, for it preserves the healing which was begun by Penance.
Of the remaining three, it is clear that Baptism which is a spiritual regeneration, comes first; then Confirmation, which is ordained to the formal perfection of power; and after these the Eucharist which is ordained to final perfection.
Reply to Objection 1. Matrimony as ordained to natural life is a function of nature. But in so far as it has something spiritual it is a sacrament. And because it has the least amount of spirituality it is placed last.
Reply to Objection 2. For a thing to be an agent it must first of all be perfect in itself. Wherefore those sacraments by which a man is perfected in himself, are placed before the sacrament of order, in which a man is made a perfecter of others.
Reply to Objection 3. Nourishment both precedes growth, as its cause; and follows it, as maintaining the perfection of size and power in man. Consequently, the Eucharist can be placed before Confirmation, as Dionysius places it (Eccl. Hier. iii, iv), and can be placed after it, as the Master does (iv, 2,8).
Reply to Objection 4. This argument would hold if Penance were required of necessity as a preparation to the Eucharist. But this is not true: for if anyone be without mortal sin, he does not need Penance in order to receive the Eucharist. Thus it is clear that Penance is an accidental preparation to the Eucharist, that is to say, sin being supposed. Wherefore it is written in the last chapter of the second Book of Paralipomenon (cf. 2 Chronicles 33:18): "Thou, O Lord of the righteous, didst not impose penance on righteous men." [The words quoted are from the apocryphal Prayer of Manasses, which, before the Council of Trent, was to be found inserted in some Latin copies of the Bible.]
Reply to Objection 5. Extreme Unction, for this very reason, is given the last place among those sacraments which are ordained to the perfection of the individual.
Source: Summa Theologica (New Advent)