What does John 7:3 mean?

Verses 3–5 present a sad commentary and produce controversy. The men in question are called Jesus' "brothers." This conflicts with the traditional myth that Mary, Jesus' mother, was a perpetual virgin. The Greek term is adelphoi, which can be used to refer to countrymen—meaning fellow Jews—as well as biological siblings. However, this same phrasing is used in verses such as Matthew 12:46 and Mark 6:3. In the gospel of Mark, Jesus' brothers are even named. Psalm 69:8 refers to "mother's sons," rather than "father's sons." This is the same passage which came to mind when Jesus cleansed the temple in John 2:13–17 (Psalm 69:9). In short, the only reasonable interpretation is that these were Jesus' physical, biological half-brothers and fellow children of His mother, Mary.

Their suggestion is that Jesus should go put on a show in Jerusalem. The feeding of thousands, from chapter 6, attracted a great deal of attention. These family members don't yet believe that Jesus is the Messiah (John 7:5). This is probably a sarcastic response to the many followers who abandoned Jesus after His preaching in Capernaum (John 6:66).

Tradition suggests that one of these brothers, James, would become a believer and write the New Testament book of James. Another brother is believed to have drafted the book of Jude. At least some of their disrespect might have been due to familiarity. Jewish tradition suggested that the Messiah would be relatively unknown (John 7:27), so merely knowing Jesus was enough for some to dismiss Him as the Promised One. As seen in the life of men like Judas Iscariot, simply knowing "about" Jesus, or being exposed to Him, is not enough to make a person a believer.