“preached the gospel to Abraham” – Abraham didn’t know about Jesus or the cross. We tend to focus on what Matt Chandler calls the “gospel on the ground” (God, man, Christ, response), but although the gospel affects each of us personally, it’s not just about us, it’s about God’s grand plan to glorify himself over the course of history as a whole, the “gospel from the air” (creation, fall, redemption, reconciliation) – God’s plan to bless all nations through Abraham.
And Abraham also serves as an example of how God would justify people throughout history, not, as Peter’s behaviour in chapter 2 suggested, by forcing Gentiles to live like Jews, but by faith.
“the man of faith” – we sometimes talk about “heroes of the faith”, and I’m not saying that’s a totally bad thing, but it can be if we focus on the man of faith instead of the real hero (the one the man put his faith in) e.g. where we read about God promising Abraham that in him all nations would be blessed, later in the same chapter we read that Abraham’s fear of the Egyptians led to him lying about Sarah being his sister, and then after we’re told that “Abraham believed God and it was counted to him as righteousness”, the following chapter tells of him going in to Hagar. Abraham isn’t a great example of faith because of how he acted, or because his faith was particularly strong, but because he was a man of faith in God. He was a man who believed God would bless him because God said so, not because of any good works he might do to merit blessing from God.