Yes, all Scripture IS inspired and useful for teaching. Who denies this? But it is not the ONLY thing useful for teaching or preserved from error.
An analogy: all bats are able to fly. But not ONLY bats are capable of flight. Most birds are, too, as well as many insects. When St. Paul says a that "All Scripture is inspired and useful," that *doesn't* limit the discussion to Scripture.
First of all, at the time he wrote those words, many books of the New Testament hadn't even been written yet. If one were to insist that St. Paul's use of the present tense was absolute, being inspired itself (as we would all agree his words were here, no?), he has just, under inspiration, rejected anything written after his words to Timothy.
Second, you fail to take into consideration somethng that has been discussed many times just in the short time I've been around this FR forum: Tradition and the magisterial authority of the Church. BOTH of which were instrumental in determining the very canon of Scripture you hold to (well, minus the seven Old Testament books and parts of others that were removed without authority in the 1500's by your spiritual ancestors).
Protestantism has NO real explanation for the canon of Scripture's existence, because it would have to acknowledge the authority of the ancient Catholic Church in its formulation. That authority was based on the God-given authority of the Church to bind and to loose, and the promise that goes with that to be preserved from error. THAT, in itself, is a source of authentic, inerrant teaching. The Catholic feast just celebrated, the Immaculate Conception, is a case in point. So is the Assumption of Mary. You don't believe in them because you have been, in effect, cut off for 500 years from the authentic teaching of Tradition in the Church.
You fail to contemplate the ancient witness of Catholicism and Orthodoxy, which are the only two forms of Christianity to have apostolicity as a characteristic of their very essence. The Orthodox differ from the Catholics in some fine points of the Assmption (we would say that that is an artifact of their separation from us for a thousand years), but they believe in the basic concept. They deny the specifics of the Immaculate Conception because they do not have the Catholic concept of original sin (perhaps another artifact of the two Church's separation), but they still believe Mary was sinless as far as "actual sin" goes. In short, here, and in many other cases, the Catholics and Orthodox demonstrate the handing-down of ancient truths of the Christian faith that Protestantism has completely lost (not just mangled a bit, but lost in total).
As I and others have said before, it takes a special arrogance for people to complain that every aspect of Catholicism is wrong when the complainer's branch of Christianity didn't even appear on the scene until the 1500's or later. Sola Scriptura may have been a convenient excuse to ignore the teaching authority of the Church, but it itself is not scriptural, and it leads to logically flawed statements like yours about 2 Timothy 3.
This is not merely a problem of semantics or differing opinions about peripherals; it is a spirituallly vital matter, since so many other things follow from it. Chief amng them, you deny the Sacraments and the whole basic nature of grace that the Catholics believe. Bluntly put, you had better be "right" about this, because, if you are wrong, you deny yourselves the basic means of both obtaining grace AND forgiveness of sins. And the constant witness of the two forms of the apostolic faith (united during the first half of the Christian Era to date), bridging the ENTIRE Christian Era, mean "nothing" to your beliefs.
When we are in-dwelt with the Ruach haKodesh,
He will illuminate the Holy Word of G-d for us.
For without the illumination of the Ruach haKodesh:
2Co. 4:3 And even if our gospel is veiled, it is veiled to those who are perishing.
2Co. 4:4 The god of this age has blinded the minds of unbelievers, so
that they cannot see the light of the gospel of the glory of
Christ, who is the image of God.
b'shem Y'shua