sorry, I misread your post - it is 180 degrees because the pitch change starts 90 degrees before max rate of pitch increase and hence max rate of flap up.
No I mean 180 degrees peak to peak.
The maximum "rate of flap up" i.e. the vertical speed is reached at the end of upward cyclic component of the aerodynamic force that is controlled by the AoA, not at its peak.
You need the gyroscopic effect to get 90 degrees peak to peak.