On occasion, particularly with hostile audiences, Jesus would make a statement and then reason with His audience as to why His statement was true.
Jesus' Equality with God: The Statement
From the NET Bible:
"The phrase ἕν ἐσμεν ({en esmen) [i.e., "are one"] is a significant assertion with trinitarian implications. ἕν is neuter, not masculine, so the assertion is not that Jesus and the Father are one person, but one “thing.” Identity of the two persons is not what is asserted, but essential unity (unity of essence)" (bible.org).
When Jesus declared that He and the Father are one, He was declaring His equality within the Godhead. From the hymn, "Holy, Holy, Holy" come the words,
"God in three persons, blessed trinity."
From Genesis chapter 1, we learn that the God of whom it is said,
"In the beginning God created the heavens and the earth" (Genesis 1:1)
is identified as Elohim. Elohim denotes a plurality, which is confirmed and underscored when Elohim says,
"Let Us make man in Our image, according to Our likeness; and let them rule . . ." (Genesis 1:26 NASB Updated).
The thrice-holy Triune God (see Isaiah 6:3) is one essence but has been revealed in three persons. In other words, God's oneness is inviolate: The Father is God, the Son is God, and the Spirit is God. His personhood, however, is expressed in a trinity of Father, Son, and Holy Spirit (see Matthew 28:19; cf. Jesus' baptism in Matthew 3:13-17; Mark 1:9-13; Luke 3:21-22; and John 1:31-34).
As Hank Hanegraaff observed in his booklet, Memorable Keys to Christian D-O-C-T-R-I-N-E,
"It is important to note that when Trinitarians speak of one God, they are referring to the nature or essence of God. Moreover, when they speak of persons they are referring to personal self–distinctions within the Godhead. Put another way, Trinitarians believe in one What and three Who's" (see Christian Research Institute's website: webmaster@equip.org).
Jesus' Reasoning Regarding His Equality with God: The Explanation
When challenged by His audience, as recorded in John 10:34-37, Jesus engages in some logical reasoning, which I call His "how much more" locution. From Constable's "Notes" in the NET Bible (again, at Bible.org):
"The clause “the Scripture cannot be broken” means that man cannot annul it, set it aside, or prove it false. It means that Scripture cannot be emptied of its force by being shown to be erroneous.
"Jesus’ statement affirms the unity, authority, and inerrancy of Scripture. Jesus held a very high view of Scripture. His point was that it was inconsistent for the Jews to claim the Old Testament as their authority (v. 34) and then to disregard something that it said because they did not agree with it. It was inconsistent for them, specifically, to stone Jesus for claiming to be God and the Son of God when the Old Testament spoke of humans as gods and as God’s sons.
“In the singular he graphe usually means a single passage of Scripture, and the verb translated broken (luo) is used in v. 18 of disregarding the letter of the law. The meaning here is ‘this passage of Scripture cannot be set aside as irrelevant to the matter under discussion’.”[385]
"Jesus did not use this argument to claim that He was God. He used it to stall His critics. He wanted them to see that the divine terms that He was using to describe Himself were terms that the Old Testament itself also used of human beings. They could not logically accuse Him of blasphemy because the Father had set Him aside and sent Him into the world with a special mission. He was a legitimate Son of God for this reason.
"As the Jews had sanctified their temple after its desecration by Antiochus Epiphanies, so God had sanctified His Son. The Jews celebrated the sanctification of their physical temple with the feast of Dedication, but they were unwilling to accept the spiritual temple that replaced it, namely, Jesus" (my emphasis).
The words in bold, above, are the essence of Jesus' argument. Jesus' reasoning was as follows:
"If the Scripture called human beings 'gods' simply because the word of God came to them (Psalm 82:6), and if they were only finite, mortal human beings, how much more appropriate is it for me, the one whom the Father set apart as His very own and sent into the world, to consider myself one essence with the Father? The saints of old were recipients of the written and spoken word of God. At this very minute you are listening to the Word of God incarnate. My question to you, therefore, is this: Why do you accuse me of blasphemy because I identify myself as God's Son?"