Why would God create beings with the capacity to sin?

"For God has bound all men over to disobedience so that he may have mercy on them all." - Romans 11:32

By looking at this passage alone, we can guess that God had set all this in motion in order to show mercy and love to all.

However, classical Christianity has always fallen silent on this mystery, we may not be intended to know why.

But the Westminster catechism at least teaches that we were intended to "love God and enjoy Him forever." If that the the end that we hold that Christianity has for us, then whatever happens here and now in the interplay of sin and free will, election and grace, is for the purpose of helping us to "love God and enjoy Him forever."

Free will is the ability of people to make choices different than God's commands.

A sin is a thought or act contrary to God's will for us.

Without the ability to sin, there is no free will.

Our problem is that free will is never addressed in the Bible. Bob DeWaay describes it this way:

Even in passages where prophets and others asked God why He allowed so much evil to harm the innocent, it was not discussed. The answer was never that God was committed to the principle of free will and determined that allowing evil was a necessary by-product of free will.

He continues:

Most free will theology is based on philosophical considerations that are imported to the discussion from outside the Bible. Since the Bible does not directly discuss the meaning of “free will,” the concept must be derived from passages about human bondage to sin and human responsibility and culpability before the Law of God. You will see this as we examine literature on the topic.

Continuing:

Free will is not the simple answer to important theological questions that people think it is. It raises more questions and complications than it answers. I set about to study this matter in great detail over ten years ago. I read the best material I could find, much of it sited in this article. The bottom line for me is that we need to accept what the Bible teaches and not try to escape from clear Biblical passages through philosophical speculation. I am not minimizing the sincere desire people have to answer the difficult question about God’s relationship to time, evil, and human choices. But I am saying that outside of Divine revelation in Scripture there are true mysteries.

it's worth the time to read all of Bob DeWaay's essay.

My personal opinion is that God considers the free will of man to be the prime directive, with everything else supporting free will. But my opinion is not supported by the Bible.

The reason God created anything at all is for His glory. (Isaiah 43:1-7 (esp v.7), Rev. 4:11, Col 1:15-16)This is a hard concept to grasp for anyone, even for a committed Christians. So the answer is that sin is there to glorify God. You may ask, "How does sin glorify God?" Sin glorifies God's attributes of justice and wrath, not His most popular attributes. Many Christians view God a pure love, and that is correct; but God is also pure wrath "a consuming fire" and pure justice. (Hebrews 12:29, Deuteronomy 32:4)

Think about it this way. If you had a family member who had been murdered by a criminal and you were present at the trial and the Judge decided to acquit the criminal despite eye witness testimony, how would you feel? Would the judge be 'glorified' in your eyes. God is glorified in the judging of sinners. In the case of true Christians, Christ stands as their sacrifice. So if we go back to the courtroom example we see the Judge's Son offering to take the punishment of the criminal and the Judge offering to take the criminal into his family to reform him.

So God is glorified by sin in two ways. He is glorified by judging sin righteously and also by His Son taking the punishment for some of the sinners.

Romans 3:22-26 (NKJV):

For there is no difference; for all have sinned and fall short of the glory of God, being justified freely by His grace through the redemption that is in Christ Jesus, whom God set forth as a propitiation by His blood, through faith, to demonstrate His righteousness, because in His forbearance God had passed over the sins that were previously committed, to demonstrate at the present time His righteousness, that He might be just and the justifier of the one who has faith in Jesus.