It didn't directly lead to the tail separating. What separated wasn't just the de-ice boot, it was the whole leading edge on the left stabilizer. That caused a stall of the left horizontal stabilizer and an increase in drag on the left side. The wings of an aircraft have a tendency to pitch the aircraft down (as they're behind the center of gravity and provide a force upwards), while the stabilizer produces a force downwards to keep the plane's pitch stable. With the loss of lift on the left stabilizer, there was less downforce (leading to a pitch down), more downforce on the right than on the left (leading to a right roll), and more drag on the left than the right (leading to left yaw).
These rather violent motions led to massive aerodynamic loads on the plane, resulting in the next failure: the left wing. When this failed, the plane violently rolled right, for reasons I'm not quite sure of (I get violently rolling, but am unsure why it was to the right). This roll stressed the plane even more, and that is when the tail ripped off the plane. The direct cause was extreme aerodynamic forces caused by the flight path, not the leading edge separation itself.