The only advice I can think of is to post part of the instructions:
"Gently hold and twist the HSF to break the adhesion seal caused by the thermal interface material (TIM) between the processor and HSF base
Note! Twist in a clock and anti-clockwise rotational direction, which creates a shear force in the thermal interface. Failure to break the adhesion seal between the HSF and the processor may result in pulling the processor out of the socket, possibly resulting in processor and / or socket damage."
You may need to repeat the process several times, carefully, until it comes loose.
Make sure there's no obvious mount or screw holding things in place.