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Did he really sacrifice him
I'm confused why you are asking, as the text seems quite clear that Isaac was not killed. The language of verses 10 and 11 ("Then he reached out his hand and took the knife to slay his son. But ...") already clearly suggests an interruption before Abraham could complete the sacrifice. This is even more clear in verse 12 ("'Do not lay a hand on the boy'", which would make no sense if Isaac were already killed) and verse 13 ("[Abraham] sacrificed [the ram] as a burnt offering instead of his son").
So, no, Abraham did not complete the sacrifice; Isaac did not die.
If you are confused by the later verse 16 ("'... because you have done this and have not withheld your son ...'"), this is not referring to an accomplished act, but rather to Abraham demonstrating that he would have followed through had he not been stopped.
Why did God command Abraham to sacrifice Isaac?
In addition to a testing of Abraham's faith (see Ray's answer), many Christians see another reason, which is foreshadowed in God's words: "Take your son, your only son, whom you love". Parents are frequently willing to give their lives for their children, and as such, sacrificing one's son, especially an only son, is perhaps the greatest sacrifice conceivable.
Jesus Christ is the only son of God, whom God loved (Matthew 3:17).
In Abraham's case, God intervened at the last possible moment and provided a substitute. But for the sake of us sinners, God himself made the ultimate sacrifice of His very own Son. Thus, many consider the testing of Abraham to be a foreshadowing of Christ's sacrifice.
Upvote:2
In Genesis 21 God made a promise to Abraham: "β¦ for in Isaac your seed shall be called", a promise Paul quoted in Romans 9:7.
Abraham knew that his descendants through Isaac would be blessed by God. There wasn't the slightest doubt about it.
Because of his faith in God's promise, Abraham understood that nothing he did, even killing Isaac, could prevent this from happening. Somehow Isaac would live and have children. The how didn't matter, Abraham simply knew that it would happen.
It's difficult to think of a stronger test of faith than this, but Abraham passed the test. And he passed it because of his faith in God's promise, not simply as a means of demonstrating it.
It's important to note that this wasn't a test of direct faith (e.g. "step onto this flimsy bridge and I'll make sure it doesn't collapse"). It was an indirect test, with Abraham having to understand and rely on the implications of an unrelated promise made at a different time.
It's traditionally thought that Isaac would have been a full-grown man by this time, perhaps 20 or 30 years old, while Abraham himself was very old. Isaac could easily have escaped the sacrifice by his physical advantage. The reason for binding him in preparation for the sacrifice was because Isaac was worried that his own faith might not be sufficient.