In your view only a regenerate person has the ability to come to Christ, it is utterly impossible for the unregenerate to be willing to come. It is not a POSSIBLE option for them.
The funny thing is, for once you gave an accurate definition of what a true choice is. You are coming along.
And as Quantum pointed out, God knows it is impossible for the unregenerate to be willing to believe if your doctrine is true. That would make God's offer empty, insincere, and even mocking of the unelect.
How anyone can believe this nonsense is beyond me.
Sorry, but I'm not going to play games with you. God could care less if you think he is fair or not. It's not possible because they are unwilling, not because God prevents them from coming.
Remember, in your view you have an atonement for everyone, yet God doesn't save everyone. Imagine if your child was in a burning building and you offered to save them, but because they said no, you watch the burn.....See, it works both ways. I'll just stick with the Scripture. The Scripture teaches that man's will is in bondage to sin. He sins because he wants to. He rejects God because he doesn't want to come. That's what the Scripture teaches. It's very fair. God has offered salvation. It is a sincere offer because God will save ALL that come to him. And insincere offer is one that God has no intention of keeping, such is not the case. God will save all that come to him. Every single person in hell will be there because they willingly choose to reject God.