I am replacing an old ceiling fan box with a new brace and box. I have the switch off and when I went to unwire the fan, the black(hot) wire is still hot? Why? I have done this procedure plenty of times and this is my first time coming across this.

If you have a fan that is controlled by a pull chain and a light that is controlled by a switch, then that is why the fan wire is still hot. It is also why you should turn off the circuit breaker before working on the circuit.

Just turning the switch off does not protect you from getting zapped.

Your switch was wired as a switch loop. Hot into the box, not through wired.