Objection 1. It would seem that not only priests have the keys. For Isidore says (Etym. vii, 12) that the "doorkeepers have to tell the good from the bad, so as to admit the good and keep out the bad." Now this is the definition of the keys, as appears from what has been said (17, 2). Therefore not only priests but even doorkeepers have the keys.
Objection 2. Further, the keys are conferred on priests when by being anointed they receive power from God. But kings of Christian peoples also receive power from God and are consecrated by being anointed. Therefore not only priests have the keys.
Objection 3. Further, the priesthood is an order belonging to an individual person. But sometimes a number of people together seem to have the key, because certain Chapters can pass a sentence of excommunication, which pertains to the power of the keys. Therefore not only priests have the key.
Objection 4. Further, a woman is not capable of receiving the priesthood, since she is not competent to teach, according to the Apostle (1 Corinthians 14:34). But some women (abbesses, for instance, who exercise a spiritual power over their subjects), seem to have the keys. Therefore not only priests have the keys.
On the contrary, Ambrose says (De Poenit. i): "This right," viz. of binding and loosing, "is granted to priests alone."
Further, by receiving the power of the keys, a man is set up between the people and God. But this belongs to the priest alone, who is "ordained... in the things that appertain to God, that he may offer up gifts and sacrifices for sins" (Hebrews 5:1). Therefore only priests have the keys.
I answer that, There are two kinds of key. one reaches to heaven itself directly, by remitting sin and thus removing the obstacles to the entrance into heaven; and this is called the key of "order." Priests alone have this key, because they alone are ordained for the people in the things which appertain to God directly. The other key reaches to heaven, not directly but through the medium of the Church Militant. By this key a man goes to heaven, since, by its means, a man is shut out from or admitted to the fellowship of the Church Militant, by excommunication or absolution. This is called the key of "jurisdiction" in the external court, wherefore even those who are not priests can have this key, e.g. archdeacons, bishops elect, and others who can excommunicate. But it is not properly called a key of heaven, but a disposition thereto.
Reply to Objection 1. The doorkeepers have the key for taking care of those things which are contained in a material temple, and they have to judge whether a person should be excluded from or admitted to that temple; which judgment they pronounce, not by their own authority, but in pursuance to the priest's judgment, so that they appear to be the administrators of the priestly power.
Reply to Objection 2. Kings have no power in spiritual matters, so that they do not receive the key of the heavenly kingdom. Their power is confined to temporal matters, and this too can only come to them from God, as appears from Romans 13:1. Nor are they consecrated by the unction of a sacred order: their anointing is merely a sign that the excellence of their power comes down to them from Christ, and that, under Christ, they reign over the Christian people.
Reply to Objection 3. Just as in civil matters the whole power is sometimes vested in a judge, as in a kingdom, whereas sometimes it is vested in many exercising various offices but acting together with equal rights (Ethic. viii, 10,11), so too, spiritual jurisdiction may be exercised both by one alone, e.g. a bishop, and by many together, e.g. by a Chapter, and thus they have the key of jurisdiction, but they have not all together the key of order.
Reply to Objection 4. According to the Apostle (1 Timothy 2:11; Titus 2:5), woman is in a state of subjection: wherefore she can have no spiritual jurisdiction, since the Philosopher also says (Ethic. viii) that it is a corruption of public life when the government comes into the hands of a woman. Consequently a woman has neither the key of order nor the key of jurisdiction. Nevertheless a certain use of the keys is allowed to women, such as the right to correct other women who are under them, on account of the danger that might threaten if men were to dwell under the same roof.
Source: Summa Theologica (New Advent)