Might I suggest that because Abraham believed God, as the word says, and the result was a fulfillment of promise, that the same can be said for any and all of us who believe. You said that the word says Christ takes away our sins. How many of us actually believe that sufficiently that it becomes a reality on day to day living? Many on this forum (and likely other forms as well...I don't know, one is sufficient punishment enough for me), believe we will continue to actively sin until the day we die. I suggest the reason for that is twofold.
One, a lack of faith in a, the power of God to accomplish such a task, or b, the unwillingness of God to do so.
Second, too many have bought into the Catholic concept of original sin, the definition of which is that we have inherited not just a fallen weakened nature as a result of sin, but sin itself. We are born sinners, and therefore we cannot cease to be sinners.
Definition B is that sin is and always has been a choice. And we have the power in Christ to choose not to.