Objection 1. It would seem that all are not bound to offer sacrifices. The Apostle says (Romans 3:19): "What things soever the Law speaketh, it speaketh to them that are in the Law." Now the law of sacrifices was not given to all, but only to the Hebrew people. Therefore all are not bound to offer sacrifices.
Objection 2. Further, sacrifices are offered to God in order to signify something. But not everyone is capable of understanding these significations. Therefore not all are bound to offer sacrifices.
Objection 3. Further, priests ['Sacerdotes': Those who give or administer sacred things (sacra dantes): cf. 1 Corinthians 4:1 are so called because they offer sacrifice to God. But all are not priests. Therefore not all are bound to offer sacrifices.
On the contrary, The offering of sacrifices of is of the natural law, as stated above (Article 1). Now all are bound to do that which is of the natural law. Therefore all are bound to offer sacrifice to God.
I answer that, Sacrifice is twofold, as stated above (Article 2). The first and principal is the inward sacrifice, which all are bound to offer, since all are obliged to offer to God a devout mind. The other is the outward sacrifice, and this again is twofold. There is a sacrifice which is deserving of praise merely through being offered to God in protestation of our subjection to God: and the obligation of offering this sacrifice was not the same for those under the New or the Old Law, as for those who were not under the Law. For those who are under the Law are bound to offer certain definite sacrifices according to the precepts of the Law, whereas those who were not under the Law were bound to perform certain outward actions in God's honor, as became those among whom they dwelt, but not definitely to this or that action. The other outward sacrifice is when the outward actions of the other virtues are performed out of reverence for God; some of which are a matter of precept; and to these all are bound, while others are works of supererogation, and to these all are not bound.
Reply to Objection 1. All were not bound to offer those particular sacrifices which were prescribed in the Law: but they were bound to some sacrifices inward or outward, as stated above.
Reply to Objection 2. Though all do not know explicitly the power of the sacrifices, they know it implicitly, even as they have implicit faith, as stated above (2, 6,7).
Reply to Objection 3. The priests offer those sacrifices which are specially directed to the Divine worship, not only for themselves but also for others. But there are other sacrifices, which anyone can offer to God for himself as explained above (A2,3).
Source: Summa Theologica (New Advent)