It's not about punishment. He's not punishing you for disbelieving in him. He's just offered you a choice: Believe in him and join him in heaven, or go your own way. A lot of people choose the latter, which unfortunately leads to hell.
That's pretty much the definition of a punishment. Just because the choice is with a person doesn't change the fact that God is handing out the punishment. That'd be like saying if I get sent to prison for murder, it's not the government that's punishing me because it was my choice to murder person X. No, I'm still being punished for my misdeed. Disbelieving in God leads to the punishment of Hell. God has detailed this punishment. It is God's punishment.