Though Jesus didn't use the exact words "I am God", that doesn't mean that He never said that He is God. One doesn't need to use the same framing of words to convey a message; the same message can be communicated in different compositions of sentences. For instance, note the following sentences which all convey the message, "I am employed."
1. I work for a Company.
2. My boss pays me well for my work.
3. I am very busy at office during the day.
4. The staff had a picnic last Saturday.
5. I would like to change my job.
So, the right kind of question to ask with reference to the doctrine of Christ's divinity would not be "Did Jesus ever use the words "I am God"?" Instead, one should ask something like, "Did Jesus ever convey the message that He was divine?" To that question, the answer is a definite "Yes." In fact, the "Yes" is too clear, because the claim to divine sonship (which the Jews understood as a claim to divinity) was one reason why the Jewish leadership condemned Jesus as a blasphemer and demanded His execution. Let's look at some of Christ's related claims:
1. "For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life. (Joh 3:16 NKJ). Jesus claimed to be God's "only begotten Son"; but, that is not all, He states that God gave this only begotten Son so that whoever believes in the Son should not perish but have everlasting life. Now, some may object that this claim was a later theological construct; not a claim by Jesus but an interpolation by the apostles. This interpolation-theory, however, is because of the prejudiced made-up mindset that Jesus was not God. It is not based on proof but on prejudice.
2. When Jesus saw their faith, He said to the paralytic, "Son, your sins are forgiven you." And some of the scribes were sitting there and reasoning in their hearts, "Why does this Man speak blasphemies like this? Who can forgive sins but God alone?" (Mar 2:5-7 NKJ). Evidently, here Jesus is doing something that the Jews were aware that only God can do. Not even a prophet or a priest could forgive a sin committed against others and against God. I can only forgive sins of those who sinned against me; but, I cannot forgive sins of those who have sinned against the Law of God; because if I do that I try to take the place of God. Jesus, obviously, knew this. But, He didn't stop just at that. He affirmed His authority to forgive sins by an act of divine power.
"When Jesus saw their faith, He said to the paralytic, "Son, your sins are forgiven you." And some of the scribes were sitting there and reasoning in their hearts, "Why does this Man speak blasphemies like this? Who can forgive sins but God alone?" (Mar 2:5-7 NKJ)
3. Now behold, one came and said to Him, "Good Teacher, what good thing shall I do that I may have eternal life?" So He said to him, "Why do you call Me good? No one is good but One, that is, God. But if you want to enter into life, keep the commandments." (Mat 19:16-17 NKJ) In this statement, Jesus not only conveys the message that no human can claim to be good or try to have eternal life by virtue of good works (for none is good), but He also forces the young rich man to reconsider his calling Jesus as the Good Teacher; for if he really believed Jesus was Good, it meant that he equated Him with God. Jesus foils the human quest for autonomy and desire to independently, by virtue of personal merit, inherit eternal life -- no one can be good apart from God. This He proves by asking the young man to sell all his possessions, distribute them to the poor, so that He will have treasures in heaven, and to follow Him,. But, the young man was not willing to part with his riches since he wished to have a life independent of God--that was impossible; it is not possible to be independent of God and have eternal life--for that would mean sin co-existing with life, which is contradictory to divine Justice:
Then the LORD God said, "Behold, the man has become like one of Us, to know good and evil. And now, lest he put out his hand and take also of the tree of life, and eat, and live forever "-- therefore the LORD God sent him out of the garden of Eden to till the ground from which he was taken. (Gen 3:22-23 NKJ)
But, by answering the question of the rich young man, Jesus has affirmed that He could authoritatively show how one could have eternal life; authoritatively, because He had eternal life. It meant both that He was Good (which no man but God was) and that He knew how one could have eternal life. He tells him to do something beyond the Old Testament command, He asks him to sell all he has, distribute it to the poor (so that he will have treasure in heaven), and to follow Him (Matt.19:21). Obviously, by asking the young man to follow Him in relation to eternal life, He is making a claim that no human can make (for "no one is good but One, that is, God.")
4."I and My Father are one."
Then the Jews took up stones again to stone Him.
Jesus answered them, "Many good works I have shown you from My Father. For which of those works do you stone Me?"
The Jews answered Him, saying, "For a good work we do not stone You, but for blasphemy, and because You, being a Man, make Yourself God."
Jesus answered them, "Is it not written in your law,`I said, "You are gods"'?
"If He called them gods, to whom the word of God came (and the Scripture cannot be broken),
"do you say of Him whom the Father sanctified and sent into the world,`You are blaspheming,' because I said,`I am the Son of God '?
"If I do not do the works of My Father, do not believe Me;
"but if I do, though you do not believe Me, believe the works, that you may know and believe that the Father is in Me, and I in Him."
Therefore they sought again to seize Him, but He escaped out of their hand. (Joh 10:30-39 NKJ)
There are a number of clauses here that convey Christ's claim to divinity: (a) He calls Himself one with the Father (b) They understand His claim as blasphemous because, as they say, "You, being a Man, make Yourself God."). (c) Jesus replies by quoting Psalm 82:6, where God calls humans as "gods"; so if He called them gods, to whom the word of God came, then why should they consider it blasphemous if the one whom "the Father sanctified and sent into the world" said not "I am God" but "I am the Son of God". Obviously, Jesus was evoking their understanding of His statements as conveying the idea of His affirmation of His divinity. They obviously knew that there was a difference between God saying "You are gods" in Psalm 82:6 and Jesus saying "I and My Father are one." The statement of Jesus clearly meant that He was claiming to be God. Secondly, He refers to Himself as the one "whom the Father sanctified and sent into the world". In other words, He was claiming pre-existence (His birth of the world was not the beginning of His life but the event of His being sent into the world). It also implies His greatness above every other human; for if those to whom the word of God came could be called "gods", then what is wrong the One who was sanctified and sent into the world calling Himself "the Son of God"? (d) Jesus also says that "the Father is in Me, and I in Him", which again provokes them to try to seize Him.
5.Then the Jews said to Him, "You are not yet fifty years old, and have You seen Abraham?" Jesus said to them, "Most assuredly, I say to you, before Abraham was, I AM." Then they took up stones to throw at Him; but Jesus hid Himself and went out of the temple, going through the midst of them, and so passed by. (Joh 8:57-59 NKJ) The message here is too clear to miss. Jesus claims in the present tense "I AM" to exist before Abraham (i.e. before Abraham was born). In other words, His existence predates the Father of the Jewish race, Abraham. Thus, though He was the son of Abraham, according to the flesh, His existence is (not was) before Abraham. The I AM (the Name of God as revealed to Moses in Exodus 3:14) also affirms that His existence is trans-temporal, that is infinite and eternal. As such, He is not a creature but the Creator. No surprise, the Jews were infuriated again by this claim and wanted to stone Jesus. For them, no existing human could claim to be greater than Abraham, their father.
Several Scriptural proofs exist for the divinity of Christ. Following are some verses that corroborate the divinity of His Person:
Pre-existence (Jn. 1:1; 1Jo. 1:1; Jn. 17:5).
Participation in creation (Gen. 1:26; Prov. 8:30; Col. 1:15; Jn. 1:3; Col. 1:16; 1Co. 8:6).
Christophanies (Gen.18,19; Hos.1:7; Gen.22,31; Exo. 3:2; Exo. 14:19; Num. 22:22; Judg.6).
2. Divine Nature
Divine Attributes (eternal- Jn. 1:1; Jn. 8:58; Jn. 17:5; omnipresent- Mt. 28:20; Eph. 1:23; omniscient- Jn.16:30;21:17; omnipotent- Jn.5:19; immutable- Heb. 1:12; Heb. 13:8)
Divine Offices (Creator- Joh 1:3; Col 1:16; Sustainer- Col. 1:17; Heb. 1:3)
Divine Prerogatives (forgives sin – Mt. 9:2; Luk. 7:47; raises dead- Jn. 5:25; Jn. 11:25; executes judgement- Jn. 5:22)
Identified with OT YHWH - I AM (Jn. 8:58; Jn. 12:41; Jn. 8:24; Jn. 8:50-58)
Divine Names (Alpha & Omega-Rev. 22:13; I AM –Jn. 8:58; Immanuel- Mt. 1:22; Lord-Mt. 7:21; Son of God- Jn. 10:36; God- Jn. 1:1; 2Pe. 1:1; Tit. 2:13; 1Jo. 5:20)
Divine Relations (Image of God- Col. 1:15; Hb.1:3; One with Father- Jn. 10:30)
Accepts Divine Worship (Mt. 14:33; Mt. 28:9; Jn. 20:28-29). Claims to be God (Jn.8:58; Jn. 10:30; Jn. 17:5 – in such case, He is either liar, lunatic, or the Lord that He claims to be, but never can be regarded as merely a good moral teacher)
Any quick perusal of the Gospels will clearly demonstrate to the unbiased mind that Jesus did claim again and again to be divine.