Acts
Acts is a historical book on the beginnings of the early Christian church. I was taught that this book is an eyewitness account by Luke himself though Acts itself never actually identifies the name of the author. It simply claims that it is written by a traveling companion of Paul. However, there are several key details that don't line up with each other.
For example, we have Paul retelling his conversion experience in Galatians where he says that he stayed away from Jerusalem for 3 years.
However, in Acts we have a different set of events
So in Paul's own words, he stayed away from Jerusalem and instead went into Arabia then back to Demascus and then finally went to Jerusalem after three years. But in Acts, we have Paul immediately heading straight to Jerusalem as soon as he leaves Damascus. And not just that, but in Galatians Paul insists that he did not see any other apostle except Peter(Cephas) and James, but again in Acts we get a different story. There, Paul is claimed to have spent time with all of the apostles.
The differences unfortunately don't end there.
In Acts 17, it mentions Paul converting some of the Jews in Thessalonica, but in 1 Thessalonians he addresses them as having "turned away from their idols." So in one instance, we have Jews, but in the other Pagans.
Only pagans worshiped idols. Paul’s converts in both Thessalonica and Corinth (1 Corinthians 12:2) were former pagans. That is why he calls him-self the “apostle to the gentiles.” There were other missionaries, in particular Peter, who were in charge of taking the message to Jews (Galatians 2:8). The Thessalonian and Corinthian churches were made up of gentiles (Paul), not Jews and gentiles (Acts).
In another instance Acts recounts Paul's meeting in Jerusalem to discuss the authenticity of his message. Acts describes this as Paul's third visit to Jerusalem, but in Galatians Paul says that it was the second time that he went to Jerusalem.
There are several more examples that can be found and that are mentioned in some of the books that I have cited. Perhaps some of them seem to be minor discrepancies, but the number of them that there are all goes towards the question: how historically reliable is the book of Acts? If the author of Acts isn't lining up with the details being explained by Paul himself, then was the author actually there? Or did the author simply do poor job of relaying Paul's timeline? If he simply did a poor job, then how can we trust the rest of the story's details? We don't have letters from Peter or other apostles to cross-verify the details. So how do we determine what is factual and what isn't?
Hebrews
We don't know who wrote Hebrews. Hebrews never states who is writing it. We also don't know when Hebrews was written. An odd point in Hebrews is that it never references anything in the Gospels. It also never references the destruction of the temple in Jerusalem that happened around 70 AD, and in Hebrews 10:1-4, the author makes an argument against temple sacrifices being a worthwhile thing. If the temple had been destroyed at the time of Hebrews' writing, then there wouldn't be any sacrifices and the argument that the author is making would be pointless.
So this book is actually one of the earlier writings, sometime around 40-60 AD. So it not only predates the Gospels, it also doesn't seem to have any knowledge of any sayings of Jesus or any of the parables.
Why do we trust a book whose authorship we don't know? Why doesn't the author of Hebrews know anything about Jesus' ministry? Why doesn't the author know any common sayings of Jesus or any of the parables? If the stories presented in the Gospels were passed down through oral tradition, then wouldn't the author be intimately familiar with them?
source: On the Historicity of Jesus, Pg. 622-623
James, 1 2 3 John, Jude
I don't want to continually belabor the same points, but scholars for similar reasons to other books also agree that these books are also written late. James is the only book that could possibly be dated to the late 60's at the earliest, but it is generally held that these books are all late first century (90 - 110).
Why do we have books that were written nearly 50 years after Paul's writings? This is almost an entire generation removed from the apostles themselves. So what authority are we listening to when we say that these books have the authority of God behind them? Who decided that these books should be in the NT and why?