Just noticed an inclusio here. Jesus appoints apostles (3:13-19) before being rejected by his immeediate family (3:20-35).
Later, Jesus is rejected at Nazareth, his home town (6:1-6), and then sends the apostles out (6:7-13).
Could it be (kite-flying time!) that the intervening section concerns why even those closest to Jesus can reject him?
Answer 1: Because the same word attracts different responses. God is not obliged to open people's eyes (chapter 4).
Answer 2: Because evil is so powerful - but Jesus is more so (5:1-20)
Answer 3: Because Jesus needs to raise the dead (5:21-43)