If I decided to go to New York on a train, I would buy a ticket and get on the train. The choice became mine. The train didn't send me there, it only took me to where I asked to go.
I think that is the same with God. We make the choice and he allows it. He made a way to let us choose "not to go", but in the end the choice is ours, not God's. It is much like when our children become adults and make choices that break our hearts if they make destructive choices. There is nothing you can do, however if they do. We can try and persuade, teach, beg even, but in the end free will wins out. God gave us free will and he won't dishonor that even if it means we are headed for eternal separation.