Festal Letter 2, section 6:Usually the way this is cited is to quote merely the following portion: "But after him and with him are all inventors of unlawful heresies, who indeed refer to the Scriptures, but do not hold such opinions as the saints have handed down, and receiving them as the traditions of men, err, because they do not rightly know them nor their power." It is stated or implied by the people providing this quotation that when Athanasius says "opinions as the saints have handed down" he means "oral tradition" or something of that kind. That's not correct.
For not only in outward form did those wicked men dissemble, putting on as the Lord says sheep’s clothing, and appearing like unto whited sepulchres; but they took those divine words in their mouth, while they inwardly cherished evil intentions. And the first to put on this appearance was the serpent, the inventor of wickedness from the beginning—the devil,—who, in disguise, conversed with Eve, and forthwith deceived her. But after him and with him are all inventors of unlawful heresies, who indeed refer to the Scriptures, but do not hold such opinions as the saints have handed down, and receiving them as the traditions of men, err, because they do not rightly know them nor their power. Therefore Paul justly praises the Corinthians, because their opinions were in accordance with his traditions. And the Lord most righteously reproved the Jews, saying, ‘Wherefore do ye also transgress the commandments of God on account of your traditions.’ For they changed the commandments they received from God after their own understanding, preferring to observe the traditions of men. And about these, a little after, the blessed Paul again gave directions to the Galatians who were in danger thereof, writing to them, ‘If any man preach to you aught else than that ye have received, let him be accursed.’
Instead, the "opinions" Athanasius has in mind is simply the Scriptures themselves taken in their correct meaning. Likewise the "them" that the heretics receive as "traditions of men" are the Scriptures, not oral traditions.
Athanasius is saying that the heretics do not know the Scriptures nor the power of the Scriptures. Therefore, instead of following the text and meaning of the Scriptures they prefer to follow the traditions of men.
This can be seen from an examination of the context preceding as well as the context following. In the context preceding:
Festal Letter 2, section 5:Notice that "the teacher delivered" refers to Paul as "the teacher." It is what Paul handed down, namely the Scriptures, that Athanasius has in mind. The heretics are those who "were men who used his words, but chose to hear them as suited their lusts, and dared to pervert them." In other words, they did not consider the words as they were written, but as they wished they were written. To put it in modern terms, they eisegeted rather than exegeting.
Oh! my brethren, how shall we admire the loving-kindness of the Saviour? With what power, and with what a trumpet should a man cry out, exalting these His benefits! That not only should we bear His image, but should receive from Him an example and pattern of heavenly conversation; that as He hath begun, we should go on, that suffering, we should not threaten, being reviled, we should not revile again, but should bless them that curse, and in everything commit ourselves to God who judgeth righteously. For those who are thus disposed, and fashion themselves according to the Gospel, will be partakers of Christ, and imitators of apostolic conversation, on account of which they shall be deemed worthy of that praise from him, with which he praised the Corinthians, when he said, ‘I praise you that in everything ye are mindful of me.’ Afterwards, because there were men who used his words, but chose to hear them as suited their lusts, and dared to pervert them, as the followers of Hymenæus and Alexander, and before them the Sadducees, who as he said, ‘having made shipwreck of faith,’ scoffed at the mystery of the resurrection, he immediately proceeded to say, ‘And as I have delivered to you traditions, hold them fast.’ That means, indeed, that we should think not otherwise than as the teacher has delivered.
Again, in the context following:
Festal Letter 2, section 7:Notice that Athanasius here clarifies what opinions of the saints he has in mind - the testimony found in Scripture, such as Luke's Gospel.
For there is no fellowship whatever between the words of the saints and the fancies of human invention; for the saints are the ministers of the truth, preaching the kingdom of heaven, but those who are borne in the opposite direction have nothing better than to eat, and think their end is that they shall cease to be, and they say, ‘Let us eat and drink, for to-morrow we die.’ Therefore blessed Luke reproves the inventions of men, and hands down the narrations of the saints, saying in the beginning of the Gospel, ‘Since many have presumed to write narrations of those events of which we are assured, as those who from the beginning were witnesses and ministers of the Word have delivered to us; it hath seemed good to me also, who have adhered to them all from the first, to write correctly in order to thee, O excellent Theophilus, that thou mayest know the truth concerning the things in which thou hast been instructed.’ For as each of the saints has received, that they impart without alteration, for the confirmation of the doctrine of the mysteries. Of these the (divine) word would have us disciples, and these should of right be our teachers, and to them only is it necessary to give heed, for of them only is ‘the word faithful and worthy of all acceptation;’ these not being disciples because they heard from others, but being eye-witnesses and ministers of the Word, that which they had heard from Him have they handed down.
Notice as well that Athanasius says "to them only" it is necessary to give heed. Notice as well that he clarifies "these not being disciples because they heard from others, but being eye-witnesses and ministers of the Word". And Athanasius has hit the nail on the head. The purpose of Luke's gospel was to memorialize the preceding oral tradition and to provide certainty to the readers.
In short, Athanasius was affirming that Scripture is not merely a human tradition, but rather the testimony of eye-witnesses and has apostolic authority, having been handed down from "the teacher."