Since its beginning, teaching has been a key part of what the Church does in the world. In fact, right after responding to Peter’s sermon on the day of Pentecost by being baptized, the very next thing it records these early disciples doing was devoting themselves to the “apostels’ teaching, and fellowship, to the breaking of bread and the prayers” (Acts 2:42). The description sounds a lot like what Christians do in worship week-by-week: teaching, fellowship, communion, and prayer.
To claim that the Church is “apostolic” is to claim that the church is still devoting herself to the study and teaching that was entrusted as a “good deposit” (2 Tim. 1:13-14) to her. That is, we as members of Christ’s Church “hold to the standard of sound teaching… in the faith and love that are in Christ Jesus.” Michael F. Bird uses the image of a tag to indicate a genuine product produced by a top level producer such as Gucci, Apple, or the NFL. Some rare collector’s items come with a certificate of authenticity. The Church’s claim to be “apostolic” is a claim to have a certificate of authenticity.
Irenaeus, an early church father, said the following:
Since, therefore, the tradition from the apostles does thus exist in the church and is permanent among us, let us revert to the scriptural proof furnished by those apostles who did also write the gospel, in which they recorded the doctrine regarding God, pointing out that our Lord Jesus Christ is the truth and that no lie is in him. (Against Heresies 3.5.1)
He also said this:
It is easy to obtain from the church since the apostles, like a rich man depositing his money in a bank, lodged in its hands most copiously all things pertaining to the truth. In this way, any person who wants to can draw from it the water of life. For the church is the entrance to life; all others are thieves and robbers. (Against Heresies 3.4.1)
Jesus came and called 12 Apostles (Mark 3:13-19). They were appointed “to be with him, and to be sent out to proclaim the message, and to have authority to cast out demons” (3:14). One of the three specific things mentioned is to “proclaim the message.” The word apostolos means “delegate” or “messenger.” Thus, when Jesus sends out the 12 to proclaim the message he is authorizing them as his special messengers. Thus, the teachings of the gospel were handed on to the Apostles directly by Christ Himself (Matt. 28:16-20; Acts 1:8; 1 Cor. 9:1; 15:7-8; Gal. 1:1). Paul also speaks of the gospel and the pattern of instruction that he himself received and passed on (1 Cor. 11:2; 15:1-3; 1 Thess. 2:13; 2 Thess. 2:15; 3:6).
In this regard, the Apostles are the foundation of the Church (Eph. 2:20; Rev. 21:14). The Church receives and hands on the apostolic tradition and teachings about Jesus: “the faith… once for all entrusted to the saints” (Jude 3). This is what followers of Jesus have been doing since the beginning (Luke 1:1-4; Phil. 4:9; 2 Tim. 1:13-14; Heb. 10:32; Rev. 3:3). We send messengers to proclaim these apostolic truths of the gospel as missionaries (Matt. 28:19-20; Luke 24:46-48; Acts 1:8). Just as the 12 were send as messengers (apostolos) to “proclaim the message,” so we are sent as messengers to proclaim the message.
Michael F. Bird, What Christians Ought to Believe, Chapter 13.
Catechism of the Catholic Church, 857-860.
Angelo Di Berardino (ed.), Ancient Christian Doctrine, 5: We Believe in One Holy Catholic and Apostolic Church.