No ---it is not arrogance if it is true. And it was true and Paul knew it to be true.
Since II Timothy was one of Paul's last epistles, he would have been fully cognizant of the fact that his previous epistles and the writings of Matthew, Luke, James that were already down on papyrus, were also holy scriptures, and that there were more to come.
Being that Timothy was probably around 20 years old when Paul wrote his 2nd letter to the youthful Timothy circa 67 AD, Timothy would have been young enough to have learned to read from many of the NT scriptures, including James' Epistle written about the time of his birth circa 47 AD. Matthew's Gospel may have been circulating when he was 5 years old, along with Paul's epistles to the Thessalonians and Galatians. At the age of 10 he would have been reading Paul's letter to the Romans, and the Corinthians.
Furthermore, note what Paul says to Timothy: "that from a child thou hast known the holy scriptures", not "when" but "from". In other words he began to read them from childhood and had continued in that practice as a young man. As the scriptures of Paul and the others grew, so Timothy grew into adulthood.
It is interesting that as the youthful NT scriptures were growing from the pens of James, Paul, Matthew, Luke --- so the youthful Timothy was growing as well. His life was probably a chronicle of the NT scriptures themselves. He probably lived long enough to add the last book of John to his canon of scripture.
Thus if Catholics really want to know who put together the first canon of scripture, they need look no farther than Timothy who knew the scriptures from a child, knew therefore what was and what was not scripture, and collected the NT scriptures as they were written, adding the new ones to the old ones. He would have been about 50 years old when he collected John's last book that closed the canon of the holy scriptures.