"Then said he (John the Baptist) to the multitude that came forth to be baptized of him, Oh generation of vipers, who hath warned you to flee from the wrath to come? Bring for therefore fruits worthy of repentance, and begin not to say within yourselves, we have Abraham to our father: for I say unto you, that God is able of these stones to raise up children unto Abraham." Luke 3:7-8
It's not just Jews and Christians that look to Abraham as the father of their nation. It is many Muslims also. It goes all the way back to Genesis 12. Abraham is the father of nations in this way. Abraham was called to be the father of many nations. Abraham begat Isaac and Isaac begat Jacob and Esau. Esau sold his birthright and Jacob received the blessing. There is also the birth of Ishmael from Abraham and the Egyptian woman, handmaiden of Sarah. Ishmael represents one nation of people and Isaac represents another, Jacob and Esau also representing many people as well as the twelve tribes of Israel from the sons of Isaac.
All of the offspring of these men claim Abraham as their father. Many are Jews and many are Muslims. They claim sonship by birthright. And children of Abraham they are. But true children of Abraham are made children of Abraham by faith not blood. It is true that Jews and Muslims can call Abraham their father by blood, but it is by faith that they/we receive the promise of Abraham. Christians (Muslims and Jews) are adopted into the promise of Abraham by faith, not blood. "For the promise, that he (Abraham) should be the heir of the world, was not to Abraham, or to his seed, through the law, but through the righteousness of faith." Please read the entire chapter four of Romans for a deeper look at justification by faith.
I think it is a wonderful thing to be born from the bloodline of Abraham. Every person, whether Jew or Muslim or other should be proud of their heritage. There is so much history and tradition handed down through many generations. But salvation comes by faith in Jesus, not a birthright through Abraham. Yes Jesus overshadows father Abraham. John the Baptist was simply telling those who placed their faith in their bloodline that it would not carry them over into the heavenlies. There are still many people today who can claim father Abraham as their progenitor that have not placed their faith in Jesus, the Father of their progenitor.