Matthew describes the human ancestry of Jesus Christ in three parts: from Abraham to David, from David to the Exile and from the Exile to the birth of Jesus (Matthew 1:17).  Matthew stresses that Jesus is at the apex of the line of faith - those people who trusted God to fulfil His promises.  Abraham clearly demonstrated that as he moved from Ur (in what is now Iraq) to the Promised Land (Genesis 12:1-5).  

Hebrews 11:8-19 highlights his faith.  But along the way Abraham also failed; he was disobedient in taking his nephew Lot with him even though God told him to leave all his family (Genesis 12:1), deceitful with the Pharoah of Egypt in saying that his wife Sarah was his sister (Genesis 12:10-20) and he disbelieved that God would give him a son through Sarah (Genesis 16:1-4).  Abraham was not the model of perfection.  But he was a model of repentance, obedience and faith, after realising his sin and failure - for which Jesus Christ would be the ultimate atoning sacrifice (Genesis 22:1-14).

The same was true of each of his successors including King David (Psalm 51:1-17). The list also includes two women who are not Jews.  Rahab the harlot (Joshua 2:1-24) and Ruth the Moabitess (Ruth 1:16-18) did not have any right to belong to God’s family - but they were hungry for God and honoured Him above themselves.  They were not only accepted among God’s people but they also both had the privilege of being direct ancestors of the Lord Jesus.

If God only selected perfect people, He would have nobody in His family, for all have sinned (Romans 3:23).  Every saint is also a sinner, but one who has been saved by grace.  Only Jesus never sinned, but He became known as the friend of sinners (Matthew 11:19).  This list of names should encourage us that God can and does use sinners who repent after failing Him.  He weaves them into the story of His people; using what He can use and refining what is unusable.  We too should be encouraged that He wants to use each of us in His story - to play our part so that His Kingdom is grown, and His glory is shown.  You may feel your sin disqualifies you from being used by the Lord: the same was true about the Biblical heroes of the faith.  The important thing is that, like them, we should repent and turn from our sin, allowing the Lord to change us so that He is glorified.