The simple answer is that the circumcision that was practiced in Abraham's day is not the circumcision practiced today, and thus not the circumcision God instituted. A "modern" Jewish circumcision involves at least two parts - Milah, Pariah, with possibly a third -Messisa. Milah involves removing the skin that extends beyond the tip of the penis. Pariah is where the foreskin is separated from the glans underneath and cut off. Messisa (also called Mezziza or Mizizah) is the third step, where the blood is sucked off the raw penis. Originally this was done by mouth, but because of the spread of disease, a tube became standard. (Messisa has fallen out of favor with all but the most orthodox Jews.)
There is plenty of historical evidence to support the idea that originally circumcision involved only Milah. Pariah was added over 2,000 years after the original covenant was made for basically political reasons. But let's also look at evidence from scripture.
When a baby is born, the foreskin does not retract, because it is adhered to the glans underneath. Click here for good illustrations of intact male anatomy (warning do not scroll down past the first two drawings if you don't want to see actual photos of adult penises). Pariah requires ripping the foreskin away from the sensitive glans underneath. In the past, the mohel would do this with a clean, trimmed fingernail. Today's mohels and doctors use various surgical instruments. The trauma to the penis is great and the chance of infection is high, so a person preforming a circumcision needs to take a great deal of care.
But look at Exodus 4:25 (New King James version): "Then Zipporah took a sharp stone and cut off the foreskin of her son and cast it at Moses’ feet, and said, “Surely you are a husband of blood to me!"" We see Zipporah, who certainly wouldn't have been trained in Pariah, cutting off her son's foreskin with a sharp stone! The NAS and NIV translate this as flint or flint knife, instead of stone.
What is a flint knife? Well, flint is a type of stone that breaks easily into pieces with jagged and razor- sharp edges. It would not have been a safe tool for the delicate separation of the foreskin from the glans. The only thing it could do safely was make a clean straight cut across the skin that hung over the tip of the penis and was not fused to it. We see the use of a flint knife again in Joshua 5:2 when God instructed the Israelites to circumcise all the boys and men that had not been circumcised while they wandered in the desert. An adult male's foreskin is no longer adhered to the glans underneath, probably making it a little safer to perform a circumcision like what is done today, but I have to ask why would they? It's a traumatic procedure and, for an adult, it has a 6-8 week recovery time! By removing only the tip of the foreskin a baby's penis, including the remaining foreskin, would be allowed to grow and develop, maintaining its normal function. An adult who was circumcised in this way would also retain the normal function of the foreskin. And as I alluded to in Part 1, retaining the function of a body part God designed is probably pretty important to Him.
I'm supposed to talk about risks. But I'm going to treat you like adults and assume that you would find out the risks before allowing your newborn to undergo a surgical procedure. Sometimes doctors gloss over these risks, so do your own research and ask lots of questions.
Now I'm going to tell you something personal about my husband (with his permission). He feels like something was stolen from him. He wishes it had been left up to him to decide, and there are a lot of men who feel that way. As a Christian, imagine your son coming to you and asking why, if he was fearfully and wonderfully made, did you surgically alter his functional anatomy right after he was born? What will you say?
So, we've covered that there are no religious reasons for Christians to circumcise and that modern circumcision is not the same procedure instituted by God, which would have fulfilled the covenant requirement while leaving the function of the foreskin intact. What modern circumcision does is remove a healthy, functional part of the male anatomy for reasons which deny the goodness of God's design. Think about it. ... and please do your research!