Dr. Pitre argues that Jesus' so-called "brothers" are actually cousins of Jesus (sons of Cleopas). The term ἀδελφός can sometimes mean cousin. While this has been a talking point among Catholic scholars for centuries, Pitre offers a robust defense of this view using evidence from the Gospels of Matthew, John and Eusebius.
This is opposite to the view I take in my The Wife of Jesus: Ancient Texts and Modern Scandals. I argue that the "cousins" (ἀδελφοὶ) hypothesis originated from an assumption of Mary's perpetual virginity. More importantly, as I discuss in the book, second and third century Christians were woefully unaware of Jesus' pre-public life and often made guesses to fill in the gaps of Jesus' life. I will also add that many of the names used in the Gospels were quite common. It is therefore very difficult to know who is who.
I confess that I am on precarious ground in making this statement as it smacks of anti-Catholicism (for which Protestant theologians have often been guilty). I am willing to be challenged along these lines. Is my reading a reaction to Catholic apologetics (thus apologetic in itself)? Or is it the most natural reading?
Two more details should be addressed. I do not think that either of these is load-bearing in and of themselves.
(1) The first is one that Richard Bauckham has underscored. Mark 6:3 reads, "Is not this the carpenter, the son of Mary, and brother of James and Joses and Judas and Simon? Are not His sisters here with us?" And they took offense at Him" (NASB). "Joses" is a diminutive form of Joseph. Could it be that this "Joses" was so-named because his father was named Joseph? Again, these names are all very common, Joseph could have been a family name.
(2) Mark 3:32-34 reads: "A crowd was sitting around Him, and they said to Him, "Behold, Your mother and Your brothers are outside looking for You." Answering them, He said, "Who are My mother and My brothers?" Looking about at those who were sitting around Him, He said, "Behold My mother and My brothers!" (NASB). There is a wordplay exploiting familial intimacy here between biological brothers and spiritual brotherhood. Does this interplay work as well with cousins?
I recommend having a look at Dr. Pitre's short vimeo linked above before commenting. Even if I disagree, I find Pitre's argument a very thoughtful and judicious way into the topic.