Why can't you earn salvation by good works?
Scripture teaches salvation cannot be earned by good works because Romans 6:23 contrasts wages and gift: the wages of sin is death, but eternal life is God's gift through Jesus Christ. Wages are what one works for and deserves; a gift is undeserved. Salvation is a gift, not earned by any work.
Les explains that Romans 6:23 sets wages against gift. Wages are what you work for; they are never a gift but what you get in return for something done. The old Adamic nature we are born with has only one direction—death, eternal death—and everything a lost person does, good or bad, piles up wages for eternal doom. The flip side is that the gift of God is eternal life. Wages are what you deserve, but a gift is what you do not deserve, and that is what salvation is. It is a gift, not something you can do one iota of work to earn; it has to be a gift.
For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.