The false myth that Joseph was a carpenter at Nazareth, a hilly fortification and suburb of the major city of Galilee, Sephoris, is due to Celsus, the arch-critic of Christianity, of the third century.
He employed all arguments, sarcasm and irony that he could to destroy the faith. His work does not survive as a whole but large parts of it are quoted by Origen in his book, Against Celsus. At one stage he made a poor, biting joke about the crucifixion. Then he added that Jesus must have been a carpenter because of the use of nails to hold him to the tree.
Origen was the foremost biblical scholar of his time. He published the Hexapla Bible giving six versions and translations of the Hebrew scriptures (possibly 6000 pages). This work supports the Greek NT and he thoroughly knew both the Hebrew and Greek texts.
What did he say about Celsus and his 'carpenter' claim? He says no scripture exists saying Jesus was a carpenter. He goes on to correct something else that will surprise many church-goers. He says that Christ was not crucified on a stake or cross. Origen is fully familiar with the NT and what Peter says several times that Jesus was crucified by being nailed to a tree (Greek xulon). He then expounds the relationship of this tree to the tree of life. That allows no doubt that he is referring to a tree, not a post.
So where did the confusion about carpenter arise? it may have been spread by a Samaritan, Justin Martyr, a few decades earlier. The Samaritans wanted to destroy all connections with the Temple and the Hebrew scriptures for their own purposes of creating a worldwide religion. Justin made the highly unlikely assertion that the family of Joseph made plows! If he had read the NT carefully, he would have found out what a bad commercial proposition that was. The real site of Nazareth was on a hill and Jesus was nearly killed by the enemies throwing him over a precipice. The side of a mountain is not the best place to make or sell plows! The great valley of Jezreel is where the crops are grown.
The word in the NT, wrongly translated carpenter in the KJV, is tekton. It means a technical specialist. It can be used of a scribe, a poet, author, ship builder etc (see Liddell & Scott). Here in a Jewish context, it means scribe and teacher, as Jesus was also called throughout the NT.
Further contextual evidence comes from the place. Nazareth was a main center for genealogical records according to Eusebius. Pedigree is highly technical and biblical. The name Nazareth comes from the Hebrew Netzer the Branch. The town's name means Branches or genealogies!
Once the "Catholic" church had gained central control Jerome muddied the waters further in his translation. He uses the Latin word faber meaning carpenter or builder. That was useful for the Roman church as it distanced Rome's responsibility for the destruction of the Temple. Jesus was a manual worker!
And what does Pilate call Jesus? Does he call him Jesus the Carpenter who must be immediately killed? What threat to the Empire or even Pharisees or Priests is a carpenter? What threat is any Galilean manual worker?
No, he and they acknowledge him as a King. Christ or Meshiach means the anointed king, like David. No one could claim the kingship without a thoroughly verified genealogy and highly technical and deep knowledge of the Bible and prophecy. If Jesus were just a manual worker of dubious parentage -- as many churches still try to maintain -- he would be laughed out of Jerusalem and probably all of Israel.