The english words in this text, “is given by inspiration of God” is only one compound word in the greek, which means ‘God-breathed’ i.e. breathed out by God.
The origin of the scriptures then is not in man, but from God, and while men were used to pen it, God was shaping them and their character for when they would write, and then leading them by the Spirit as they wrote.
Not only does this apply to the OT, but the NT. The Apostles were promised that the Spirit would guide them into all truth (John 16:13). Most of the NT was written infallibly by the Apostles, and those that weren’t were overseen by Apostles, like Mark and Luke.
As a result, it is infallible, inerrant, and subsequently profitable for study, and you cannot be a Christian unless you take it seriously in all of its teaching.