Yes, the Bible does say that some day we'll become perfect -- but only when we get to Heaven. Then all sin will be banished, and we will be perfect, "holy and blameless in (God's) sight" (Ephesians 1:4).
Until then sin is an ever-present reality, both in our lives and in the world around us. Sin isn't just something we do wrong; sin is like a "spiritual virus" infecting our whole lives and robbing us of our moral and spiritual strength. Only one person was completely free from sin's grip, and that was Jesus Christ. Even the Apostle Paul -- the greatest Christian who ever lived -- admitted that sin still had a hold on him: "I have the desire to do what is good, but I cannot carry it out" (Romans 7:18).
Does this mean we should just give up and not try to fight sin's pull on us? No, certainly not! Jesus Christ came not only to forgive our sins, but to set us free from sin's grip by the power of His Spirit within us. Have you turned your life over to Christ? If so, ask Him to help you turn from sin and follow His will every day. And if you haven't committed your life to Him, ask Him to come into your life today -- and He will.
Remember: We aren't saved because we're perfect -- for we're not, nor will we be this side of eternity. We are saved solely by God's grace, through faith in Jesus Christ. And some day our battle with sin will be over and we'll be with Him forever.