The truth is, a Christian's holiness is hidden outside himself in Christ through faith.
Nothing upsets the egotism of Old Adam more than when he's told: "your righteousness isn't worth anything to God and none of your works get you one inch closer to salvation." Old Adam's self-love is so profound he will do anything to put himself in a position to give the Almighty everything He needs to grant Old Adam salvation. Every act of piety, even the best he has to offer, is the Old Adam confession of self-love. And to say, "Only faith that looks up to the Lamb of God at Calvary, only faith which receives all things from Jesus saves," disgusts Old Adam. Old Adam, not Jesus, must stand at the center and be the measure of all things. Even a Christian's holiness and works are received through faith in Jesus. As a tree produces fruits because it's limbs are fed by the sun and its roots watered, so a Christian is a "good tree" by virtue of his being in Christ through faith. Holiness isn't something to be achieved and works aren't what he does to prove he's a good tree. Just as with faith, a Christian is holy and produces fruits because God's Spirit works through the Gospel and Christ's gifts to produce good works in and through him. He trusts that he is a branch and Jesus the vine. Of course, Old Adam considers this impossible, since he's not making the choice for himself. He isn't in control of what his holiness looks like and which good works he decides to do.
But, the truth is, a Christian's holiness is hidden outside himself in Christ through faith. Only God sees a Christian's good works, and then only by his faith and what creates faith: God's Word and the sacraments. Everything a Christian does is done in Christ and because he is an instrument of Christ.
Old Adam's other religions can teach that they do the same works as Christians. They love their neighbor like Christians. They perform acts of charity like Christians. They live lives of devotion to God like Christians. But, they cannot claim to be in Christ through faith. Even though non-Christians may claim to works that are holier and "better" than Christians' works, it doesn't earn them a better relationship with God. It doesn't earn them salvation.
Others, like Jews and Muslims, can be praised for their holiness. A Jew can prove he is more obedient to the commandments than Christians. Likewise, if a Christian is "Christian" because he demonstrates to the world his holiness or his obedience to God's commands, what distinguishes him from any other religious man? That's why, in Christ, a Christian does not talk about his holiness, or his works, or his obedience or abilities. He only speaks about the Lamb at Calvary. He puts his hope solely in Christ.
But, Old Adam must be at the center of everything. He is a giver, not a receiver. He is a doer of deeds, not one who prays to be done unto. He chooses his works, he is not an instrument through whom God does good works (never of Old Adam's choosing). Passivity in relation to God, Old Adam argues, threatens to undo everything he's worked for: righteosuness, sanctity, piety, a Christian life worthy of God's favor. His optimism about his own abilities and his self-love drive Old Adam to treat as enemy anyone and anything that causes him to doubt himself. He refuses to accept that Jesus "became to us wisdom from God, righteousness and sanctification and redemption" because if he is going to brag about anybody it's not going to be Jesus. It's going to be a boast in his accomplishments by which he has earned God's attention.
On the other hand, a Christian trusts that the fruits of faith are the fruits God's Spirit produces in and through him, when and where the Spirit chooses. Then, at the Last Day, he will ask, "Lord, when did we see you hungry and feed you, or thirsty and give you drink? And when did we see you a stranger and welcome you, or naked and clothe you? And when did we see you sick or in prison and visit you?" And Jesus will answer, "Truly, I say to you, as you did it to one of the least of these my brothers, you did it to me."
The Christian life is hidden in Christ through faith. In Christ, the Christian receives all he needs for body and life. He looks to the Lamb at Calvary and rejoices that faith, charity, holiness, and works are all given to him as gift on account of Jesus' bloody suffering and death. All produced in and through him by God's Spirit. All his hope, all his certainty, all his comfort located in Jesus, and nothing of himself does he lean on for salvation. Nothing of Old Adam's egotism. Nothing of earning or deserving. Just Christ alone, the center and measure of all things.