Let me take a stab at this one, no pun intended:
What kind of general would send his men to battle, knowing full well that many of them might die?
Hopefully, one who had a broader perspective and could see the sacrifice as a means to accomplish some greater good.
Perhaps this is what God had in mind with Abraham and Isaac. But, what "greater good" could possibly be accomplished by Abraham nearly sacrificing his beloved son?
Maybe God was trying to remind Abraham (and everyone who reads the story in the Bible) of His love for mankind, "for God so loved the world, that He gave His only begotten son...(John 3:16). However, in God's case, the sacrifice was ultimate. There was no substitute ram in the thicket.
So, OWK, you unknowingly answered your own question: ..to prove that He (God) loved him (Abraham, and by extension all of us)