what it means is, if you taught me what baptism is, how it is to be performed and who is to be baptized, i would understand what you believed about baptism. since you are not an Apostle, i am free to disregard what you believe.
however, if someone was taught by the Apostle Peter, Paul or John and we know that person was ordained to the episcopate, then that person’s writing can be trusted to convey the teaching they received directly from an Apostle.
it is how the “universal” or “catholic” faith was developed. since the Apostles traveled the known Roman world preaching the same Gospel, someone in Syria, Turkey, Greece, Egypt, Rome, India, Jerusalem, etc. etc all received the same faith, the catholic faith.
None of your church fathers was taught by an Apostle...And here's what the Apostles said about your church fathers...
2Co 2:17 For we are not as many, which corrupt the word of God: but as of sincerity, but as of God, in the sight of God speak we in Christ.
And
Gal 1:6 I marvel that ye are so soon removed from him that called you into the grace of Christ unto another gospel:
Gal 1:7 Which is not another; but there be some that trouble you, and would pervert the gospel of Christ.
Gal 1:8 But though we, or an angel from heaven, preach any other gospel unto you than that which we have preached unto you, let him be accursed.