The story of Abraham and Sarah in Genesis chapters 16-21 was familiar to Paul’s readers as he applied it to their struggle.  Could they simply believe in God’s promise of forgiveness and acceptance, or did they have to struggle by their own efforts to earn their place in heaven?  One thing was certain: while Hagar and Ishmael lived together with Sarah and Isaac (Genesis 21:8-21) there could be no peace.  Even though Abraham wanted to keep both children (Genesis 17:18), it was not possible, and God told him to send Hagar and Ishmael away.  

It was a difficult decision for Abraham. But he had to choose.  It was the perfect example for Paul to show to the Galatians: they also had to choose – either trust in Jesus Christ alone or pin their hopes on living a perfect life – they could not do both.  
 
It is a common error for people who want to believe in Jesus also to believe that they will not be accepted unless they ‘work their passage’ to heaven.  It is an old satanic lie.  Adding anything to the finished work of Christ will strip it of its potency.  Our good deeds, our prayers and religious habits have absolutely no power to ensure our salvation; otherwise we would be able to claim to have earned God’s favour and proudly boast of our own holiness.  

But God does not allow us to do that (Ephesians 2:8-9).  Salvation is a very humbling experience.  We do not deserve God’s favour at all, but He gives it by His grace because of His great love (Ephesians 2:1-5); that is why we praise Him.   Those who work for their salvation can only praise themselves – but only for a short time until they realise that they have no salvation at all.