Why not sin?
(1) "Live as people who are free," this verse says. This isn't pretending to be what you're not; it's living out what you are! You are no longer a slave to sin. You have been bought back, redeemed by the precious blood of Christ (1 Peter 1:18). Do you still feel enslaved? Then bank on this truth, reckon on it: in Christ you are free. God's word declares it, so believe it, looking to Jesus for the freedom He gives (John 8:31,36). Focus on your poor condition of ups and downs is pride: self is preeminent in your thoughts. Instead, set your mind on Christ and the truths of freedom in Him, and look to no other.
(2) Being freed, you are not free. After all, you have been bought by Someone. Being free from condemnation, can you live however you want,doing evil? Nothing of the sort! We are not just saved from sin and it's sentence, death. We are saved to righteousness (Romans 6:16-18). We are now servants of God. Just as the "foolishness" of God is wiser than the best wisdom man has to offer (1 Cor 1:25), so in bondage to God we are freer than in the "freedom" of "doing what we want."
(3) You are a servant of God. Just as employers want to use people who are qualified for the work, so God wants to use people who are qualified. 2 Timothy 2:20-22 describes our usefulness in direct relation to fleeing youthful lusts, and "pursuing righteousness, faith, love, and peace, with all those who call on the Lord from a pure heart." Again, it's not just fleeing lusts, but moving on to something: things that please our Lord, namely, righteousness, faith, love, and peace.
Bonus: The verses that follow our key verse in 1 Peter give practical examples of exactly those things. Read through the rest of the book and see which categories the instructions fit into: righteousness, faith, love, or peace.