Chaffey in "Defense of Easter" at 30, cites James to help answer the question in his chapter 3 title: "Did Jesus appear to any skeptics?"
"For whatever reason, James did not believe in Jesus as the Messiah prior to the Resurrection. In fact, none of his brothers believed in HIm early on (John 7:5). On one occasion they even tried to prevent Him from speaking, thinking He was out of His mind (Mark 3:20-21, NET). However, just several weeks after the Crucifixion they were counted among his followers"
In context, John 7:5 appears to be implying that Jesus' brothers did not merely fail to believe in him as messiah, their disbelief motivated them to mock Jesus for making such a claim:
1 After these things Jesus was walking in Galilee, for He was unwilling to walk in Judea because the Jews were seeking to kill Him.
2 Now the feast of the Jews, the Feast of Booths, was near.
3 Therefore His brothers said to Him, "Leave here and go into Judea, so that Your disciples also may see Your works which You are doing.
4 "For no one does anything in secret when he himself seeks to be known publicly. If You do these things, show Yourself to the world."
5 For not even His brothers were believing in Him.
6 So Jesus said to them, "My time is not yet here, but your time is always opportune.
7 "The world cannot hate you, but it hates Me because I testify of it, that its deeds are evil.
8 "Go up to the feast yourselves; I do not go up to this feast because My time has not yet fully come."
9 Having said these things to them, He stayed in Galilee. (Jn. 7:1-9 NAU)
Notice, Jesus' brothers tell him to go do his works in Judea where his disciples are, despite Jesus' brothers not believing in him (notice also the brothers admit Jesus has disciples or followers elsewhere, yet still don't believe him).
How could they be telling Jesus go do his miracles in Judea, if they didn't believe his claims were true? There's a plausible explanation: They had the same attitude toward Jesus that today's skeptics have toward the many fake miracle workers in Christianity today, i.e., "go to the local children's hospital and cure all the diseases and cancers! (i.e., "show yourself to the world", "do something that will permit the world to examine your claims"). When alleged miracle-workers are addressed like this by skeptics, it is clear the skeptics are talking with a bit of mockery, and do think there is the slightest possibility that the advice will be taken, or that the miracle-working claim is true.
Notice also: the brothers tell Jesus to do this and thus "show Yourself to the world", again, they seem to be taunting him..."if your miracle claims are true, do them in a manner that increases the likelihood that your critics can see your works too, do them out in the open!"
It is clear from this context that v. 5 is a significant summary statement that the unbelief of Jesus' brothers was not simply a lack of belief, but a highly confident attitude that Jesus' claims were more than likely false.
They taunted Jesus at this point in their lives the way conservative Christians and skeptics taunt prosperity gospel preachers who claim ability to do miracles:
If that's really true about you, do your miracle in a non-controlled context!
The purpose of Christians and skeptics taunting that way is: if you follow our advice, your claims of ability to do miracles will be put to the acid test. If you can really do miracles, then why would you fear doing them in a context specifically created to guard against trickery and fraud as much as possible?
13 And He went up on the mountain and summoned those whom He Himself wanted, and they came to Him.
14 And He appointed twelve, so that they would be with Him and that He could send them out to preach,
15 and to have authority to cast out the demons.
16 And He appointed the twelve: Simon (to whom He gave the name Peter),
17 and James, the son of Zebedee, and John the brother of James (to them He gave the name Boanerges, which means, "Sons of Thunder ");
18 and Andrew, and Philip, and Bartholomew, and Matthew, and Thomas, and James the son of Alphaeus, and Thaddaeus, and Simon the Zealot;
19 and Judas Iscariot, who betrayed Him.
20 And He came home, and the crowd gathered again, to such an extent that they could not even eat a meal.
21 When His own people heard of this, they went out to take custody of Him; for they were saying, "He has lost His senses."
22 The scribes who came down from Jerusalem were saying, "He is possessed by Beelzebul," and "He casts out the demons by the ruler of the demons."
23 And He called them to Himself and began speaking to them in parables, "How can Satan cast out Satan?
24 "If a kingdom is divided against itself, that kingdom cannot stand.
....31 Then His mother and His brothers arrived, and standing outside they sent word to Him and called Him.
32 A crowd was sitting around Him, and they said to Him, "Behold, Your mother and Your brothers are outside looking for You." (Mk. 3:13-32 NAU)
If we assume all that inerrantists must assume Jesus' family had experienced up to this point, then the negative view of Jesus held by his mother and brothers becomes more incredible than a miracle:
Jesus' mother had experienced angelic visions explaining she would conceive Jesus solely by the Holy Spirit.
Luke 1:26 ff. Some would argue this was a literal meeting since "vision" is not implied in the text, rather v. 26 speaks about Gabriel going to Mary physically.
Jesus' step father Joseph had a similar vision. Matthew 1:19 ff.
For inerrantists who say belief in Jesus' virgin birth is essential to salvation, this implies Mary and Joseph and Jesus would have revealed to others right at the beginning of his ministry the miracle of his birth.
The fact that Mark in 1:10 can write about Jesus at baptism seeing heaven opened and the spirit descending on him like a dove, makes it likely this was something made known to Jesus' immediate family and followers early on.
Jesus was apparently gone for 40 days in the desert being tempted by the devil and having angels minister to him (Mark 1:13), so it is reasonable to assume he would inform his family upon return how he managed to stay alive that long.
Jesus must have been doing things convincingly showing he was messiah early on, as when he calls Andrew and Peter, they drop everything and follow him, Mark 1:18, so do the others (v. 20).
Jesus created a stir in the synagogues, and in such collectivist society, surely word of such rabbinical dazzling traveled fast, his mother would certainly have heard of it. Mark 1:21-22
Jesus healing a demoniac, v. 27, creating such a debate about his powers that the news of him spread early and fast throughout Galilee (v. 28).
He heals Peter's mother-in-Law (v. 31)
He heals many more people (v. 32 ff)
He continued to cast out demons throughout Galilee (v. 39)
He heals a leper, and despite warning to keep it quiet, news of it spread so much that Jesus could not even enter a city without causing dangerous overcrowding by those following him around (v. 45)
When he returns to Capernaum several days later, large crowds gather at his door so much that the only way Jesus can heal a paralytic is by removing a section of the house roof and lowering him down into the house (2:1-4)
Jesus healed the paralytic to the amazement of these large pressing crowds (v. 12)
Jesus then is found reclining in the house of a tax-collector, Mark saying there were many such people following Jesus (2:15)
Jesus heals a man's withered hand to the knowledge of the Pharisees (Mark 3:1-6)
Jesus healed innumerable people as large crowds followed him in Galilee, Jerusalem, Idumea, beyond Jordan and in the vicinity of Tyre and Sidon7 Jesus withdrew to the sea with His disciples; and a great multitude from Galilee followed; and also from Judea (Mk. 3:7-10)
All of these events are presented by Mark as taking place before the point where his mother and brothers are said to think Jesus has lost his senses in 3:21.
But if the gospel of Mark is telling the historical truth (i.e., that all of Jesus' alleged miracles done before 3:21 were genuinely supernatural and literal facts of history), how likely is it that despite the crowds believing in him, Jesus' own family thinks he is capable of losing his senses?
Writing for the inerrantist-driven New American Commentary, inerrantist J.A. Brooks admits that the "his own" of 3:21 refers to Jesus' mother and brothers, and that they believed he had gone insane:
3:21 In the Greek text the subject of the first two clauses is literally “those with him.” The KJV and RSV (1st ed.) interpret this to mean “his friends,” the NASB and NKJV “his own people,” and the RSV (2nd ed.), NRSV, NEB, REB, and NIV “his family.” In view of vv. 31–32 the last of these is certainly correct. The idea that Jesus’ family opposed him troubled some ancient copyists who changed the text to read, “When the scribes and the rest heard.” The concern of Jesus’ family was not likely limited to his physical needs (v. 20); they probably were more concerned about the family’s reputation because in their estimation Jesus was acting in a fanatical and even insane way. The same verb is used in Acts 26:24 and 2 Cor 5:13 and means literally to stand outside of oneself. The verb translated “to take charge” means to arrest in 6:17; 12:12; 14:1, etc. Evidently they intended to seize Jesus and force him to return to Nazareth with them.
Brooks, J. A. (2001, c1991). Vol. 23: Mark (electronic e.). Logos Library System;
The New American Commentary (Page 73). Nashville: Broadman & Holman Publishers.
It is interesting that the notion that Jesus' family thought him insane, troubled some ancient copyists sufficiently that they arbitrarily corrupted the text. Apparently, Jesus' family thinking him insane was not easily harnonized with other Christian doctrine.
21 “His people” renders an ambiguous Greek construction (οἱ παρ᾽ αὐτοῦ) which generally means “envoys” or “adherents” but on occasion can mean “relatives” (e.g., LXX Prov 31:21; Taylor, 236). Wansbrough (NTS 18 [1971–72] 234–35; similarly Wenham, NTS 21 [1974–75] 296–97) has recently argued for “adherents,” meaning the Twelve, to be the more natural reading. Accordingly, Jesus’ disciples go outside to control the excited crowd. This reading, however, fails to take several factors into consideration, not least of which being the evangelist’s “sandwich” structure of 3:20–21 and 3:31–35 around 3:22–30. Mark 3:31 makes clear that Jesus’ “family” is the subject of 3:21.
e.g. exempli gratia, for example
LXX The Septuagint, Greek translation of the OT
NTS New Testament Studies
Guelich, R. A. (2002). Vol. 34A: Word Biblical Commentary : Mark 1-8:26.
Word Biblical Commentary (Page 172). Dallas: Word, Incorporated.
Jesus’ family in Nazareth has been informed about his exhaustion from dealing with the crowds, and they are concerned about his well-being and distressed that people are pressing upon him so that he is not even able to eat (3:20–21). This alone would not account for their urgency, however, in deciding to travel thirty miles to take charge of him and declaring that he is “out of his mind.” Jesus is behaving oddly according to their expectations and is not only doing but saying strange things. They consider him on the verge of a mental breakdown and are ready to take him back to Nazareth for rest and recuperation. Well-intentioned, their concern arises from a misunderstanding (similar to that of the scribes) of his mission.
Elwell, W. A. (1996, c1989). Vol. 3: Evangelical commentary on the Bible.
Baker reference library (Mk 3:13). Grand Rapids, Mich.: Baker Book House.
Or, they did not view him as any more significant than Benny Hinn is viewed by his own family members. Yes, he makes a big show, and yes he has a lot of followers claiming he can heal, but at the end of the day, he's nothing but a charismatic religious fanatic.
If Jesus' own family didn't believe him to be God up to this point, this strongly boosts the liberal position that Jesus's godhood is a fiction added by later writers to the gospel material.
It's rather easy to see why Chaffey did not spend any time whatsoever on the question of how Jesus' own family could disbelieve his claims early in his ministry. You cannot get into the biblical data without being forced to conclude that they were either correct to reject his claims, or they were unbelievably thick-headed.