The fact that the Bible is sometimes inconsistent and contradictory is PROOF that it hasn't been tampered with over the centuries, and has come down to us unedited, warts and all..
Atheists are further confused because they prefer to forget that the Bible consists of two parts, the Old and New Testaments, and as any sunday school child can tell them, Jesus overules the Old T..
"The covenant of which Jesus is mediator is superior to the old one" (Heb 8:6)
As for the authorship of the gospels, we know enough about the writers to be able to do a "This is Your Life" show about them-
Matthew the disciple, formerly Levi (Mark 2:14; Luke 5:27) son of Alpheus, was formerly a tax collector (Luke 5:29-30) one of the 12 apostles handpicked by Jesus (Matthew 9:9), he wrote his gospel between c.60 and 80 AD after Mark wrote his first.
Mark, a friend of Jesus's righthand man Peter (1 Peter 5:13) also called John, Mark was a cousin of Barnabas (Colossians 4:10), a helpful co-worker of Paul (2 Timothy 4:11), and wrote his gospel c.60AD not long after some Apostolic Letters were written: i.e., James, Galatians, 1 and 2 Thessalonians, 1 & 2 Corinthians, and Romans. His mother was one of the Marys (Acts 12:12) from an influential and probably wealthy family, and so some speculated that the last supper was held in their home and that he was the young man in Mark 14:51-52 which is not in the other accounts.
Luke, a doctor (2 Tim. 4:11) and a gentile convert (Luke 1:2) probably by Paul who became his traveling companion (Acts 17:1; 20:5, 6-21:18 ). He wrote his gospel c.65 AD.
John the disciple, (John 13:23) son of Zebedee, the brother of James the "greater" (Matthew 4:21; 10:2; Mark 1:19; 3:17; 10:35) wrote his gospel c.95AD, the last to be written before Revelation. Also from a wealthy family (Mark 1:20; Luke 5:3; John 19:27). His mother was probably Salome (Matthew 27:56; Mark 15:40). He was one of the closest disciples to Jesus among the twelve (Matthew 17:1; 26:37; Mark 5:37; 13:3). He was zealous (Matthew 20:20-24; Mark 3:17; 10:35-41; Luke 9:49, 54). He became one of the leaders of the Jerusalem Church (Acts 15:6; Galatians 2:9) and of the seven churches in Asia (Revelation 1:11). He was banished to the island of Patmos where he wrote Revelation.