Why did Abraham keep believing God would give him a son when it was physically impossible?
Abraham kept believing because he trusted God's repeated promise, not physical possibility. Though he was a hundred and Sarah ninety, he had genuine hope, knowing that God, who calls things that are not as though they were and quickens the dead, would somehow bring the promised son to pass.
Les explains that verse 18 says Abraham "against hope, believed in hope," meaning against common sense. Abraham was a hundred years old and Sarah was ninety, yet God kept telling him he would have a son and that a nation would come from his body. It seemed ridiculous to the human intellect and to the physical understanding of reproduction, but Abraham had genuine hope and knew God would somehow bring it to pass. Les ties this to verse 17, where God is described as the One who quickeneth the dead and calleth those things which be not as though they were. That is God's prerogative, as in creation, where He created everything out of nothing; only God can take nothing and make it something. Les also applies it spiritually: we're nothing, but God makes us something. And, as Les notes, we know God did bring it to pass.
Who against hope believed in hope, that he might become the father of many nations, according to that which was spoken, So shall thy seed be.
More Questions
Why did Abraham believe God would give him a son even when it seemed impossible?
Abraham had genuine hope and believed, even though the promise seemed ridiculous to human intellect and physical understanding, because he knew God would bring it to pass.