You're completely ignoring, or purposefully leaving out, God's responsibility for his creation. God, as the creator of all things, is responsible for all things. God created hell and the criteria by which souls are judged to go there, so he's responsible for anyone who goes.
A much better analogy is a mafia boss. A mafia boss offers his protection, but if you don't accept it he's going to have his boys shoot out your kneecaps. Now, did you choose to have your kneecaps shot for refusing his protection? No, that's ridiculous, the mafia boss is obviously responsible for what happened.
What if someone tries to rob you on the street at gunpoint, meaning he'll shoot you if you don't give him your wallet. He says "don't make me shoot you." If you don't give him your wallet did you choose to get shot, or is the thief responsible for pulling the trigger to shoot you?
You can't ignore God's position as the authority and one responsible for his entire creation. Your analogies completely ignore that fact.