Objection 1. It would seem that original sin does not infect the will before the other powers. For every sin belongs chiefly to that power by whose act it was caused. Now original sin is caused by an act of the generative power. Therefore it seems to belong to the generative power more than to the others.
Objection 2. Further, original sin is transmitted through the carnal semen. But the other powers of the soul are more akin to the flesh than the will is, as is evident with regard to all the sensitive powers, which use a bodily organ. Therefore original sin is in them more than in the will.
Objection 3. Further, the intellect precedes the will, for the object of the will is only the good understood. If therefore original sin infects all the powers of the soul, it seems that it must first of all infect the intellect, as preceding the others.
On the contrary, Original justice has a prior relation to the will, because it is "rectitude of the will," as Anselm states (De Concep. Virg. iii). Therefore original sin, which is opposed to it, also has a prior relation to the will.
I answer that, Two things must be considered in the infection of original sin. First, its inherence to its subject; and in this respect it regards first the essence of the soul, as stated above (Article 2). In the second place we must consider its inclination to act; and in this way it regards the powers of the soul. It must therefore regard first of all that power in which is seated the first inclination to commit a sin, and this is the will, as stated above (74, A1,2). Therefore original sin regards first of all the will.
Reply to Objection 1. Original sin, in man, is not caused by the generative power of the child, but by the act of the parental generative power. Consequently, it does not follow that the child's generative power is the subject of original sin.
Reply to Objection 2. Original sin spreads in two ways; from the flesh to the soul, and from the essence of the soul to the powers. The former follows the order of generation, the latter follows the order of perfection. Therefore, although the other, viz. the sensitive powers, are more akin to the flesh, yet, since the will, being the higher power, is more akin to the essence of the soul, the infection of original sin reaches it first.
Reply to Objection 3. The intellect precedes the will, in one way, by proposing its object to it. In another way, the will precedes the intellect, in the order of motion to act, which motion pertains to sin.
Source: Summa Theologica (New Advent)