These verses are part of a longer passage (Galatians 2:11-21) which started by Paul explaining why he had challenged Peter to stay true to the gospel and stop pulling others back to religious legalism (Galatians 2:11-13).  The Law of Moses could never save anybody; it could only define sin and accuse people who broke the law.  But when Jesus died, He was punished for all sins and so the law has no more power to accuse those who are safe in Christ.  

And more than that, Paul said that he identified so closely with Christ, that His death was Paul’s death too.  In other words, Paul considered that he should have a deathly unresponsiveness to sin’s demands.  His former life of self-glorifying religious zeal had no place in a relationship with Jesus Christ, especially as Jesus now lived within him (Romans 6:6).  The old life had to go because he was now a new creation in Christ (2 Corinthians 5:17).   
 
By contrast, Paul’s physical life was now being lived out in the power of God, with the indwelling company of Jesus Christ.  The life of Jesus was evident in Paul’s body, enabling him to advance the Kingdom of God and sacrifice himself in many ways, joyfully (2 Corinthians 11:23-28).  The grace of God had transformed Paul’s life; there was no reason at all to go back to that guilt-ridden religion, especially as Jesus had loved him so much that He died to save him.  To try to earn his way to heaven would be to despise God’s grace, and he could never succeed anyway (1 Corinthians 15:9-10).
 
There is a simple choice.  Either live a totally perfect life, or trust in Jesus and rely on God’s grace to save you.  There is no real contest logically, because we know that we are prone to sin.  Trying to be good can never take away the bad; and if even a tiny bit of bad remains, it will disqualify us from heaven.  So, like Paul, we have to live each day trusting that Jesus has taken our sin away, and we rely on Him to strengthen and guide us so that we can be His agents of love and light in this dark and wicked world.  We may feel unworthy, and we are!  But if we trust in Jesus we are counted worthy of being His friend for ever.  Tell this good news to your other friends (invite them to see www.crosscheck.org.uk).