But he turned, and rebuked them, and said, Ye know not what manner of spirit ye are of.
Note 2 at Lu 9:55: Jesus was constantly being accused of breaking the Law of Moses (see list of six instances where Jesus was accused of breaking the Sabbath in note 5 at Joh 5:9). He taught differently than the Law of Moses (Mt 5:21-48), and here He rebuked His disciples for desiring to do what an Old Testament prophet did with God's blessing and power. However, Jesus didn't come to destroy the Law but to fulfill it (Mt 5:17).
The Law was given to kill and condemn (2Co 3:7-9), to release the wrath of God (Ro 4:15), and to impose the curse (De 28:15-68 and Ga 3:10-13). Elijah was operating under this dispensation of the wrath of God when he called down fire from heaven and it consumed 102 men (2Ki 1:9-12). It was the fire of God that fell, not the fire of the devil (2Ki 1:12). God was releasing His wrath and punishment on sin through Elijah, as He did on other occasions in the Old Testament (Ex 12:29-30, 14:19-31, 32:26-28; and Nu 16:23-35).
However, Jesus came not to destroy people's lives but to save them (Joh 3:16 and 10:10). "God was in Christ, reconciling the world unto himself, not imputing their trespasses unto them" (2Co 5:19). Jesus was just in doing this because He bore our sins (Isa 53:4-6) and the accompanying wrath of God (Mt 27:46 and Heb 2:9). Jesus didn't reject God's judgment against sin; He bore it (2Co 5:21). Therefore, He was able to extend the grace and mercy of God to those who would have been doomed under the Law of Moses (Ac 13:38-39).
The Old Testament Law was like a judge passing sentence upon sin. Jesus became our advocate (or lawyer, 1Jo 2:2), and even more than that, He became our substitute, bearing "our sins in his own body on the tree" (1Pe 2:24). He didn't destroy God's judgment; He fulfilled it in Himself so that we could go free.
This forever changed God's dealings with sinful man. In light of what Jesus has done in the New Covenant, we would be rebuked for trying to release God's wrath upon others as was done in the Old Covenant. Likewise, if Jesus had been on the earth in His physical body reconciling the world unto Himself in the days of Elijah, then Elijah would have been rebuked for his actions in 2Ki 1:9-15. There is a difference between Old Testament Law and New Testament grace. "For the law was given by Moses, but grace and truth came by Jesus Christ" (Joh 1:17).