In Catholic theology "inspiration" is a technical term. An inspired book is one which has God as its primary author. Apostolic Scripture falls into this category because even though God wrote it through human agency, he chose the actual words of Apostolic Scripture.
Is Apostolic Tradition inspired? In one sense it is, but in another it isn't. When God initially revealed doctrines to the apostles he determined the form in which these teachings came to them, so the original giving was inspired. But God did not directly fix the way the apostles expressed these teachings to others. The apostles might express a single doctrine from God in a variety of ways. So while the original giving of Apostolic Tradition was inspired, the words in which it has been passed down to us are not inspired.
The Word of God was Orally Transferred
In Mark 16:15 - Jesus commands the apostles to preach the Gospel to every creature. But Jesus did not want this preaching to stop after the apostles died, and yet the Bible was not compiled until four centuries later. The word of God was transferred word of mouth or orally. Jesus told his disciples to preach but did He say write it down?
Sola Scriptura Is Wrong
This teaching was spread by Martin Luther , the Protestant Reformer. This belief is based on Paul's writing in 2 Timothy 3:16-17 which says
In 2 Thessalonians, Saint Paul talks about keeping the tradition which were taught by them.
Protestants use this verse all the time to reject using Tradition . Actually Jesus talks about Tradition that have been perverted by the elders. Not the Tradition the Apostles taught since Jesus was the one that gave them the traditions.2 Thess. 3:6, "Now we command you, brethren, in the name of our Lord Jesus Christ, that you keep aloof from every brother who leads an unruly life and not according to the tradition which you received from us."
This Tradition from the Elders is the one talked about in the Gospel of Saint Matthew . In the passage from the Gospel of Saint Matthew, Jesus clearly address who made up the particular Tradition. In that Passage it didn't say "Tradition of the Apostles" it says "Traditions of the Elder".Mark 7:8-9, "Neglecting the commandment of God, you hold to the tradition of men.9He was also saying to them, You nicely set aside the commandment of God in order to keep your tradition."
In Paul's Writing, he talks about the Scripture in his letter to Timothy.Matt. 15:1-6 "some Pharisees and scribes came to Jesus from Jerusalem, saying, 2"Why do Your disciples transgress the tradition of the elders? For they do not wash their hands when they eat bread." 3And He answered and said to them, "And why do you yourselves transgress the commandment of God for the sake of your tradition? 4"For God said, Honor your father and mother,' and, He who speaks evil of father or mother, let him be put to death.' 5"But you say, Whoever shall say to his father or mother, "Anything of mine you might have been helped by has been given to God," 6he is not to honor his father or his mother.' And thus you invalidated the word of God for the sake of your tradition."
Even Protestant scholars often appeal to Tradition....you have known the Holy Scriptures, which are able to make you wise for salvation through faith which is in Christ Jesus. All Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness, that the man of God may be complete, thoroughly equipped for every good work (2 Timothy 3:15-17).