Well, we know that many of the sons of Apostolic succession have failed to follow God's guidance, so how can you know for sure that all of the writers of scripture followed it in full? Did the writers of scripture have a special grace not given to future Bishops?
The Catholic Church has never claimed that individual bishops are inerrant.
But I understand your dilemma: because you reject the idea that the Holy Spirit has ever guided the Church that compiled and finalized the New Testament, you have no logical reason to believe that the New Testament is inerrant.
The canon of scripture was thouroughly debated among the fathers of the Church, and it was established by ecumenical councils. Much was rejected. The role of apostolic succession was in that it determined who the bishops of the Church were that established the canon.