When they start the 'rotate' maneuver, the nose of the aircraft doesn't immediately go to (for instance) 10 degrees. It's a progression.
As soon as the nose starts pitching up (by 1 degree for instance), the aircraft is already generating lift to pull the aircraft up.
If the speed is set right (so you're fast), when you get to that 10 degrees angle of attack, your tail has already cleared the runway by a very safe margin, because you've been producing X lift from 0 to 10 degrees of rotation.
However, if your speed is set too slow, you're not generating as much lift, so the aircraft will be pulled up slower (you have been producing Y% less lift from 0 to 10 degrees of rotation). This means that by the time you reach your designated 10 degrees of angle of attack, you haven't cleared the tail yet, and it will hit the runway.
(Note that you can't keep increasing AoA indefinitely if you need more lift; at a critical speed, the airflow will separate from the wing and stop generating any lift. That's an aerodynamic stall.)