If we were to believe the accusation that John was, in reality, Elijah, we would have to believe in reincarnation since John had a normal type of birth. For Elijah to be John he would either have to be reincarnated into Elizabeth's womb, or he would have had to appear on the scene as an adult. Therefore, the statement that John is Elijah needs to have another explanation that I believe is stated by Gabriel when he speaks to John's father Zechariah.
So now our question is, In what sense is John the Baptist to be identified with or as Elijah"?
The angel Gabriel announced to Zechariah, John's father, that his son's name would be called 'John' in Luke 1:13. (Luke 1:13 But the angel said to him, "Do not be afraid, Zacharias, for your petition has been heard, and your wife Elizabeth will bear you a son, and you will give him the name John.) He goes on to say in verse 15 that he will be great in the sight of the Lord and "shall drink no wine or strong drink and will be filled with the Holy Spirit from his mother's womb.'
Verse 17 says that, "he will also go before Him (referring to the Lord Himself) in the spirit and power of Elijah, which is a ministry of reconciliation, the hearts of the fathers turned to the children and children turning to their fathers." Notice that the angel identified John and his future ministry among the people as "in the spirit and power of Elijah".
In Matthew 11:13, Yeshua states: 'For all the prophets and the Law prophesied until John." (Yeshua calls him "John" not 'Elijah", who is included as part of all the prophets.) In verse 14, Yeshua says "and if you are willing to receive it, he is Elijah who is to come".
Yeshua pointed to John the Baptist as the fulfillment of Elijah's coming but he was not a reincarnation. This is proven in John 1:20 when the Jews sent out the priests and Levites to investigate John's ministry. They ask him if he is the Messiah. He states emphatically 'No !' They ask him again if he is Elijah and John answers "I am not."
This was not a temporary memory loss for John that Yeshua had to correct later. In verse 25, John the Baptist is asked 'Why do you baptize if you are not the Messiah or Elijah or the prophet? In verses 25-27 John points to the Messiah who is coming after him. He states that it is he who is the forerunner of Malachi 3:1. In Luke 1:76, we see that John's father, Zechariah is filled with the
Holy Spirit and says that his child will be called the prophet of the highest and will "go before the face of the Lord and prepare His ways again.' ("And you, child, will be called the prophet of the Most High; For you will go on BEFORE THE LORD TO PREPARE HIS WAYS;)
This relates John's ministry to Mal. 3, and Luke 1:17. John labored in the spirit and power of the former prophet by calling people to repentance and preparing them for the salvation that Messiah would bring.
Let's now sum up:
It's obvious that when Yeshua spoke in Matt. 11:13-14 concerning John being "Elijah who is to come" He was not speaking in a solid, literal sense. Yeshua was metaphorically comparing two different things that also shared some similarities and functions. The Jewish scriptures always taught resurrection, not reincarnation. Each person is given one body to live in and will be reunited with that same body in the resurrection.
When one takes the whole body of scripture instead of isolating verses, we find the consistent teaching that refutes any concept of Elijah becoming John the Baptist and then becoming Elijah again.