I am searching! I do not want to defend a belief. But it is true that many Muslims believe that the person whom Abraham sacrificed was Ishmael, and they claim that It is mentioned in the Messianic prophecies, The one who is supposed to be the savior comes from the generation of the one who was supposed to be sacrificed by Abraham.
Therefore, it is purely wishful thinking for Muslims to use the rites of the Hajj as proof that Abraham offered up Ishmael at Mecca near the Kabah, since pre-Islamic history indicates that these rites were nothing more than pagan customs adopted by Muhammad into Islam. Further, as was noted, Islamic scholarship strongly disagrees and much confusion still exists over the identity of the son, with some arguing for Isaac and others for Ishmael.
The lack of uniformity of opinion and the ambiguity of the Quran in regard to this issue helps to solidify the Biblical narrative as vastly superior and more trustworthy.
Finally, the Quran gives no clear reason why God would test Abraham in this fashion, and yet the Bible does. Abraham and Isaac were shadows of what was to eventually come nearly two thousand years later on the same mountain site where Isaac was offered.
Just as Abraham displayed unconditional love for God in his willingness to sacrifice his one and only son, God also gave up his only beloved Son on the cross of Calvary to prove to the world that He is the true source of unconditional, infinite love. Whereas God withheld the hand of Abraham from completing the sacrifice, He did not withhold his own hand from sacrificing his only Son, going to the extremes in displaying his love for mankind, an extreme that even Abraham did not cross.
Interestingly when Abraham was leading Isaac to the mountainside, Isaac asked his father where the Lamb was that was to be sacrificed, to which Abraham replied, "God will provide himself the Lamb for a burnt offering, my son." (cf. Gen. 22:7,8)
Yet instead of finding a Lamb, a ram was given. (cf. Gen. 22:13) This is primarily due to the fact that the Lamb of God was to arrive two thousand years later:
"The next day he (John) saw Jesus coming toward him, and said, ‘Behold, the Lamb of God who takes away the sin of the world!’ ... ‘Behold the Lamb of God’." (John 1:29,36).
Here was the Lamb of God sent to atone for the sin of the world. This is the awesome ransom that the Quran alludes to: Jesus Christ, the Eternal Word of the Father, offering himself as a ransom of infinite value, covering the debt of sin from beginning to end and throughout eternity.
Tabari notes that the Islamic practice of animal sacrifice done in commemoration of Abraham and his son, "wards off an evil death, so sacrifice, O servants of God!" (2: p. 96).
How much more, then, will Christ's sacrifice atone for mankind's wickedness seeing that man's worth is far greater in the eyes of God than animals. Because Christ is the Eternal Word animal sacrifices are no longer needed, since Christ's atonement is sufficient for all time:
"When Christ came as high priest of the good things that are already here, he went through the greater and more perfect tabernacle that is not man-made, that is to say, not a part of this creation. He did not enter by means of the blood of goats and calves; but he entered the Most Holy Place once for all by his own blood, having obtained eternal redemption. The blood of goats and bulls and the ashes of a heifer sprinkled on those who are ceremonially unclean sanctify them so that they are outwardly clean. How much more, then, will the blood of Christ, who through the eternal Spirit offered himself unblemished to God, cleanse our consciences from the acts that lead to death, so that we may serve the living God! For this reason Christ is the mediator of a new covenant, that those who are called may receive the promised eternal inheritance - now that he has died as a ransom to set them free from the sins committed under the first covenant." (Hebrews 9:11-15).
"But this man, after he had offered one sacrifice for sins forever, sat down at the right hand of God." (Hebrews 10:12).
Thus, Abraham and Isaac were shadows of the things that were to come, pointing to the Father and Son's willingness to sacrifice themselves in the greatest display of love the world has ever seen; the Father's willingness in sacrificing his eternal love, with the Son giving up his own life on behalf of fallen humanity:
"For God commendeth his love toward us, in that while we were yet sinners Christ died for us." (Romans 5:8 R.S.V.).
"... For God is love. In this the love of God was made manifest among us, that God sent his only Son into the world, so we might live through him. In this is love, not that we loved God but that he loved us and sent his Son to be the expiation for our sins." (1 John 4:8b-10 R.S.V.).
This is indeed the greatest love story the world has ever known:
"For God so loved the world that he gave his only Son, that whoever believes in him should not perish but have eternal life." (John 3:16 R.S.V.).
I would urge you to read this link-and welcome to the forum.