A Gun At Your Head
Suppose that a man holds a gun to your head, and tells you to rob a bank or he will shoot you. Regardless of what you think about free will, you can still decide not to rob the bank and be shot. But if you do rob the bank, you won't be responsible because you were coerced.
A Space Alien Controls Your Brain
Suppose there is a space alien in orbit around the earth in an invisible space ship. Suppose that he has some very advanced technology such that he can reach into your brain and control everything you do. He has you rob a bank. Presumably it is clear that you do not have free will, because your actions are controlled by something outside your body. But since nobody knows about the space alien, you will be held responsible for robbing the bank.
Simulating the Future
It is, of course, impossible to simulate (and hence predict) the exact future of everything, because that would require a computer bigger than the entire universe, and it still wouldn't run in real time. But it is still possible to predict localized futures of isolated simple systems for near futures, with high probability. Otherwise we couldn't do science.
The system I describe here is certainly beyond our ability to predict today, but may well be possible some day. You enter a room containing a screen and two buttons, labeled A and B. You are instructed to wait five minutes and then push one of the buttons. As you enter the room, a computer scans your body and various relevant properties of the room. After four minutes, the computer displays “You will push button A” on the screen. After another minute, you push button B. You do this because you believe you have free will, and you think this proves it.
What's wrong with this picture? The computer must simulate the entire five minutes. The simulation must include the display of the result that occurs after four minutes, because it is one of the inputs to the simulation. But it hasn't finished the simulation yet, so it doesn't know what to put into the simulation at that point. If you think this through, you will realize that it is impossible to write such a program.
However, if we take away the screen, and just print the result on a printer outside the room, the problem goes away. There is no reason to believe that such a result could not be computed with better than 99 percent accuracy. When you leave the room, and see the result, you may find it hard to believe that it was printed before you pushed the button, but I'll just leave this for you to ponder.