The "fig tree," without fruit, represented fruitless Israel. Christ had sought fruit for three years, and had found none[Luke13:6-9]. There was nothing but leaves. Thus, the tree was to be "cut down", with a view to the Church being called into existence to bring forth fruit in relation to the kingdom of the heavens, in the stead of Israel [Matt. 21:43].
And, though Israel would be restored at a future time, Israel could never again be placed in the fruit-bearing position in relation to the heavenly sphere of the kingdom[Matt.12:31,32]. The nation, through a failure to bring forth fruit in this realm, had forfeited this right forever. Israel, when restored, can only bring forth fruit in relation to the earthly sphere of the kingdom
Thus, in Genesis, fig leaves only, apart from the figs themselves [fruit], depicted man's condition following the fall. He was in a fallen state, in no position to bring forth fruit relative to the reason surrounding his creation. Then, in the gospel accounts, Israel, though in a position to bring forth fruit surrounding the reason for the nation's existence[ as Gods first born son,in possession of the passover lamb], didn't bring forth fruit. And Christ used a fig tree without leaves only to respresent not only Israel's condition at that time [fruitless] but to also show, through the cursing of the fig tree, what was about to befall Israel.