According to "On Free Choice of the Will" why did God give us free will if it leads to sin? Did not God then indirectly create sin?

This is one of the most difficult theological questions, a question that has perplexed some of the finest minds ever since the dawn of Christianity; so we're not going to be able to decide the matter here. However, that doesn't prevent us from offering up some suggestions that you might like to consider.
According to established Christian teaching, God has given each and every one of us the gift of free will. More than anything else, this is what makes us human. If we didn't have free will, one could argue, then we simply wouldn't be human; we'd be automata or robots. Or perhaps we'd be like puppets, manipulated and controlled by God using invisible strings.
So as humans we have free will. But with that divine gift comes certain responsibilities, and all too often we fail to discharge them. Free will can easily be abused, and when this happens, according to Christian teaching, we are led into sin. Sin is easier to understand if you look at it as a general condition, an estrangement from God rather an individual act of transgression.
In the book of Genesis, Adam and Eve introduce sin into the world by defying God. Like every other human, they were given the power of free will; but they abused it when they ate of the Tree of Knowledge. This act of willful disobedience led them to be expelled from the Garden of Eden into a world of sin, where we—their ancestors—now live.
The story of Adam and Eve illustrates the relation of free will to sin. God gave humankind the gift of free will out of his love for us. But we chose to abuse free will, leading us to a state of sinfulness. So it is human beings, and not God, who are directly responsible for sin. God could well have ordained that humans would not sin, that they would only use the gift of free will for good. But if that were the case, then we wouldn't really be human at all. As mentioned earlier, we'd be little more than robots.