The key to interpreting Mt. 7:13,14 is the concept of life that Jesus uses. The basic meaning of life is existence. Jesus, however, presents to Israel something that goes far beyond just the opposite of non-existence. Already in the book of Exodus, God promised Israel through Moses that they would become a special nation of kings and priests (Ex. 19:5,6). The Apostle Peter then writes to the Gentile believers that this promise does not only apply to Israel in the flesh, but because of their unbelief it has been presented to believers from outside this nation (1 Pt. 2:7-10). What is important in the context of Mt. 7:13-14, Peter informs us in an introduction to his letter that it is “an inheritance that can never perish, spoil or fade. This inheritance is kept in heaven for you” (1 Pt. 1:4 NIV).
The term 'eternal life' often appears in the Gospels (eg. Mt. 19:29, Jn. 3:15-16, 3:36, 5:24, 6:40,47). Eternal in the sense that it does not end; that it is not subject to death. In Jn. 5:26 our Lord defines immortality as 'having life in itself'. The Father has such life, the Son also has such life, and such life is the hope of the chosen nation. The condition for receiving immortality, however, is conversion to God through Jesus Christ. Just two lines earlier, the Lord assures us: "Very truly I tell you, whoever hears my word and believes him who sent me has eternal life and will not be judged but has crossed over from death to life" (Jn. 5:24 NIV). The condition of faith and obedience to the word was expressed in Mt. 7:13,14 as the choice of the narrow road.
Jesus says of himself: "I am the way and the truth and the life. No one comes to the Father except through me" (Jn. 14:6 NIV). Therefore, the goal of entering the narrow road represented by our Lord is coming to God, returning to fellowship with Him. By accepting Jesus Christ, we cease to be 'children of rebellion', whom we are while living in disagreement with the principles of divine justice, and we become children of God in whom God's spirit works (Rom. 8:14-16; Eph. 2:1-6). Being thus born of the holy spirit, we also receive a new, unhampered life that will become our eternal property, if we persevere to the end and fill the fruit of righteousness (Rom. 6:9-11, 8:5-11; Flp. 1:9-11).
Few of Israel have entered the narrow road through faith in Jesus Christ, so according to the Lord's words, their lot is destruction. However, this is not about eternal death - a person who is condemned to death in Adam cannot be condemned to death for the second time. A person who lives can be condemned to death. In the eyes of God, however, only those live who are born again of the holy spirit through repentance and conversion (Romans 6:1-11). This rebirth was not experienced by the unconverted Jews who rejected Jesus.
In what sense, however, has the Jew rejecting Jesus experienced 'destruction' - it will be helpful here to reach for the Greek language, where the equivalent of our 'destruction' is apoleia, which occurs in two basic meanings: 1) annihilation, and 2) loss. The fact that it also has the second of these meanings is clearly testified by Mt. 26:8 and Mk. 14:4, where we read about the loss /waste of oil. A Jew who did not accept Jesus did not experience apoleia in the first sense - if that were the case, the entire 11th chapter of the letter to the Romans would be meaningless. However, he experienced apoleia in the second meaning, i.e. he really lost the possibility of obtaining immortality in the glory of the divine nature, he lost his eternal life.
Finally, it needs to be stressed that our Lord did not come to Israel for judgment, he did not come to give verdicts about life and death. If one hears his teaching but does not believe, he will be judged on the basis of the Lord's teaching “at the last day”, i.e. at the next day of judgment. This will be the time when 'the word will be the judge', i.e. on the basis of this teaching, humanity will be instructed, tested, and punished, as well as the final verdict will be issued on this basis (Jn. 12:47,48 NIV). This also applies to Israel as it is shown in the already mentioned 11th chapter of the letter to the Romans, especially in the passage Rom. 11:25-32. The goal of the Lord's first coming is to make the reward of the eternal life accessible. The condition, however, is obedience, hence the 'loss' that has been incurred by the greater part of the chosen nation.