You leave out the rest.
John 1:19-23
They asked him, "Then who are you? Are you Elijah?"
He said, "I am not."
"Are you the Prophet?"
He answered, "No."
Finally they said, "Who are you? Give us an answer to take back to those who sent us. What do you say about yourself?" John replied in the words of Isaiah the prophet, "I am the voice of one calling in the desert, 'Make straight the way for the Lord.' "
So why did he refuse to call himself Elijah, but instead give a verbal clue? Because John knew, like the Messiah, that his ministry would be rejected. You also take the verses out of order. The second passage was the one above...the third passage is this:
Matt 17:10-13
The disciples asked him, "Why then do the teachers of the law say that Elijah must come first?"
Jesus replied, "To be sure, Elijah comes and will restore all things. But I tell you, Elijah has already come, and they did not recognize him, but have done to him everything they wished. In the same way the Son of Man is going to suffer at their hands." Then the disciples understood that he was talking to them about John the Baptist.
You can't get with it my friend,even your shell game can't save you this time
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In order to understand the new testament passages under discussion we need to go back to the old testament original prophecy regarding Elijah:
According to the Old Testament book of II Kings, Elijah the Prophet had ascended "into heaven" in a "chariot of fire." (see: chapter 2) This spectacular event supposedly happened about 850 years before Christ. Later, in about 450 BC, Malachi prophesied that this same Elijah, who had ascended into heaven, was also going to return from heaven to herald the coming of the Messiah:
.... Behold, I will send you
Elijah the prophet before the coming of the great and dreadful day of the LORD" -Malachi 4:1-5
The Jewish religious leaders of Jesus' day were well aware of the 'return of Elijah' prophecy. At one time the rabbis had asked Jesus' disciples to explain how Jesus could possibly have been the Messiah when it was obvious that Elijah had not returned from heaven yet.
The Apostles couldn't answer this question, so they asked Jesus:
"Why do the Jewish leaders insist Elijah must return before the Messiah comes?"
Jesus answered by first affirming that this question was valid and that this prophecy indeed was true. He said:
"They are right. Elijah must come and set everything in order..."
But then, to everyone's surprise, Jesus explained:
"In fact, he [Elijah] already has come, but he wasn't recognized, and was badly mistreated by many... Then the disciples realized he was speaking of John the Baptist."-Matthew 17:10-13 (LIVING BIBLE-CATHOLIC EDITION) (this account can also be found in: Mark 9:11-13)
Clearly, Jesus taught that this was a true prophecy. Jesus agreed that Elijah indeed "must return before the Messiah comes." But then, to the surprise to everyone there, Jesus claimed that John the Baptist was the fulfillment of this prophecy.
How, could John possibly have been the return of Elijah? Malachi didn't say anything about Elijah's return being in some mysterious, unrecognizable way. Neither does he say that some other man is going to be born hundreds of years later and that this man somehow was going to be the return of Elijah. Instead, Malachi clearly says that Elijah himself was going to return. That's not a difficult concept to visualize. Elijah ascended into heaven in a chariot of fire. And he's going to come back. Visibly. Physically. In the flesh.
One of the strongest testimonies that John is not Elijah is on the Mount of Transfiguration (Matt. 17:3; Luke 9:30; Mark 9:4-5). Elijah and Moses appear and Jesus talks to Elijah. The disciples recognize him as Elijah in his original form, not as John the Baptist. One must either concede that they are 2 different people or that John the Baptist turned back into Elijah. To claim that Elijah is John the Baptist is to teach reincarnation. The premise is that a spirit in a former body comes back to be born in another body. At the very least, it is transmigration. The Bible has never taught this. In II Kings 2:1, we find Elijah taken bodily into Heaven. For one to enter Heaven they must be transformed (1 Cor. 15:50-54), changed to an immortal body, a body which is no longer subject to death since corruptible flesh cannot enter into Heaven. If Elijah came back as John the Baptist, and was killed, this would be impossible according to Scripture. For one who has had a changed body to be equipped for Heaven, does not turn back to mortality. If we look at it more carefully in II Kings 2:11 Elijah never experienced physical death so for him to come back in another body means he reincarnated not only in Spirit but in body too, and the Bible never teaches either one of these. Elijah did not die, so the Scripture is not talking about his reincarnation as John the Baptist (2 Kings 2:1,11).The Bible teaches resurrection, a totally different concept.
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OT Misquotations -- (1) MATT. 3:3 ("For this is he that was spoken of by the prophet Esaias (Isaiah--Ed.), saying, 'The voice of one crying in the wilderness, Prepare ye the way of the Lord, make his paths straight") is an inaccurate translation of Isa. 40:3 RSV ("A voice cries: In the wilderness prepare the way of the Lord, make straight in the desert a highway for our God"). Nothing is said in Isaiah about one crying in the wilderness.
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Malachi 4:5-6.Behold, I will asend you Elijah the prophet before the coming of the great and dreadful day of the LORD:
6 And
he shall turn the heart of the of fathers to the children, and the heart of the children to their fathers, lest I come and smite the earth with a curse.
it very interesting that John the Baptist, who apparently was standing in for a preoccupied Elijah, was supposed to have been trying to reconcile families as stipulated in Malachi 4:5-6. Yet, there is not one reference to John the Baptist ever attempting to perform that required function.
. To make matters worse, Jesus claimed in Luke 12:49-53 that his mission was to divide families.
So we have John the Baptist portrayed as Elijah by the New Testament writers who is supposed to have a mission to reconcile families and Jesus having a mission to divide them. A more absurd set of mission parameters for two men living at the same time, allegedly directed by the same God, I can't imagine. This is the type of nonsense that occurs when writers attempt to concoct and retrofit an agenda or storyline into an existing prophecy as the New Testament authors did.
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There is yet a final falsehood to notice in this wonderful NT passage
"But I say unto you, That Elias is indeed come, and they have done unto him whatsoever they listed], as it is written of him." Mark 9:13
first: the death of John is ascribed directly to Herod Antipas,Not the jews as Mark 9:13 claims
(Matthew 14:10). "He [Herod Antipas] sent and had John beheaded in the prison"
second: Mark 9:13 Bless us with imaginary prophecy :
they have done unto him(John the baptist or Elijah ,whatever you wish to call him) whatsoever they listed],
as it is written of him."
Question: where is it written in the old testament that (John the baptist or Elijah) will be killed etc as Mark claims (mark 9:13 they have done unto him as it is written of him) ???????
Yet, despite this flaw and the many others noted, millions of people consider this Book a remarkable example of divine word. In reality, the only remarkable thing about it is that so many intelligent people could have been duped into believing that it was remarkable.
mg: 
Jesus makes clear in Matt 17:11, Elijah is still to come.)