The Jehovah's Witnesses have published in their literature their explanation - that the religious leaders who accused him of trying to make himself God misunderstood. In their New World Translation of John 10:33, they have those leaders saying, “because you, although being a man, make yourself a god.” This is also in their 2006 book, The Greatest Man Who Ever Lived, section 81, giving the JW explanation as to why there were further attempts to kill Jesus. After quoting that verse, the book asks,
“Since Jesus never claimed to be a god, why do the Jews say this?”
JWs say that Jesus was not God, but “a god”, and have rendered John 1:1 that way too. However, your question is not about that, but as to why JWs say religious leaders back in the day misunderstood Jesus as claiming to be God. Even if that is taken to include the idea that Jesus was “a god”, which would also warrant stoning to death in the view of those religious leaders, why do the JWs claim that they had misunderstood Jesus? That book states:
“The Jews, however, overlook the fact that Jesus acknowledges
receiving authority from his Father. That Jesus claims to be less than
God, he next shows by asking, ‘Is it not written in your Law [at Psalm
82:6], ‘I said: “you are gods”? If he called ‘gods’ those against whom
the word of God came,… do you say to me whom the Father sanctified and
dispatched into the world, ‘You blaspheme,’ because I said, I am God’s
Without going into any argument as to why Jesus’ quoting of that Psalm need not mean what the JWs think it means, the outstanding question is, why did his explanation not pacify the Jews so that they realised Jesus was not claiming to be God? According to the NWT rendition of Jesus’ next comment, those who ‘misunderstood’ him would have had it completely cleared up when he added, according to their NWT,
“…believe the works, in order that you may come to know and may
continue knowing that the Father is in [union with] me and I am in
[union with] the Father” (John 10:38).
That could not be clearer, could it? Jesus was apparently denying being God but only claiming to be in union with God the Father. Why, those religious leaders would likely make the same claim of themselves! They were appointed god-like status as representing God on earth, entitling them to respect (not stoning to death), and they were zealously seeking to act in union with God.
This shows that the NWT has Jesus effectively denying being God. The NWT does not give reasons for that slant, but masses of JW literature reiterates their belief that Jesus had a starting point in time, being the first and only direct creation of Jehovah as the Word. This is the basis for their renditions of John 1:1 and 10:33, 38, and why they won’t have Jesus taking the Divine Name, the I Am, to himself.
The problem of how those religious leaders could have possibly continued to ‘misunderstand’ Jesus’ claims here simply increases with the NWT rendition of events. According to the NWT, Jesus is really denying being God. He is making clear that he is merely ‘a god’ and only ‘in union with’ God – not “in God” as all other translations of the Bible state. By changing “God” to “a god”, and “in him” to “in union with him”, that is the same as Jesus saying, “I’m not God! Why are you trying to kill me? I’m not God!”
Of course, we all know that the Bible nowhere has Jesus saying, “I am not God,” but the NWT in those verses comes as close as it can to that. Not because the JWs have misunderstood the words of Jesus, any more than those religious leaders back then did, but because they cannot have their rendition of the Bible saying in any sense that Jesus is God, and that he is in the Father, as the Father is in him. Thus, the NWT tries to have Jesus portrayed as “a god” and saying he is merely “in union with the Father.”
If that is correct, then in the NWT Jesus disabused those religious leaders of a false notion, that he was claiming to be God. He would have taken all the wind out of their sails, and none of them would have picked up a stone to kill him. It is only according to other translations that we see they did not misunderstand Jesus. They knew full well that Jesus was claiming to be God.