When one becomes convinced of the existence of God and rejects Him, then one chooses hell.
Hypothetically speaking, what if Allah is real and you find yourself burning in hell for all eternity for worshiping Yahweh? Did you choose hell? No, you tried to choose heaven.
Atheists don't make a choice. They don't choose heaven or hell because they believe in neither. Our disagreement lies with what it means to actually "choose" something. Clearly, your definition differs from ours. But your definition of choice is used to justify the punishment of nonbelievers. It's easy to paint God as all loving when it's not his fault most people burn in hell for all eternity, because those who burn chose it. But that's not how choice works. Nobody chooses to suffer for all eternity. Nobody says, "You know what, I'd rather suffer in hell than be happy for the rest of existence." Your definition of choice implies people WANT to burn for all eternity.
Even if you argue one can choose something they don't want, the argument falls flat. Your use of the word choice would make the following statement true. "Jennifer chose not to use a condom, therefore she chose to get pregnant", even when Jennifer didn't want to get pregnant but was too anxious to have sex to worry about protection. This use of the word choice I dislike, but if this is the version you're using, then you still have to admit that people who "choose" hell without actually wanting to go to hell are being punished for being ignorant.
And that's the problem. You want to make it sound like people choose hell, so when they burn God can't be blamed. But if people burn in hell for rejecting God, they burn for being ignorant regardless of how you use the word "chocie"