O on A Osteokinematic vs Arthrokinematic Relationship

I am reviewing the Cervical revolution text and have a question. Page 46 in the grey box first point: Lateral Pterygoid pulls ipsilateral base of sphenoid down and forward while the ipsilateral (what the text states) OR contralateral (what seems correct) greater wing simultaneously raises? 

In OA osteo kinematics section the O rotates contralaterally to lateral flexion, Atlas goes opposite and Axis follows O (p31.) But in Arthrokinematics section Lateral flexion of O on A with conjunct contralateral O rotation, alar ligaments causes ipsilateral axial rotation and contralateral atlas rotation (atlas follows O.) Can you explain this? I cant seem to make it right in my head. 

Page 46 is correctly written and holding a model of a sphenoid or looking at a 3-D image of one would possibly help understand the relationship of the lower base of the sphenoid to the greater wing.   I can appreciate the difficulty you may have in their relationship.

The first sentence on page 31 relates only to Occipital (O) movement on the Atlas (A) in lateral flexion if the axis of the spine in general is in a neutral position. Often this is not the case. In a neutral position the last sentence on page 31 is also correct.  However, keep  in mind the mechanics of C1, or the atlas, on C2, or the axis, or C2 movement on C1 could  be challenged in lateral flexion if the lateral flexion of O on A or A on O occurred on a cervical spine that is positionally  laterally flexed to the right or to the left.

In the Arthrokinematic section of the Cervical Revolution manual, page 37 compliments page 31.  The top of page 38 is also correctly written with respect to the alar ligament and soft tissue in general.  Our control and stability of the O on A and the A on O depends on this counter balance provided by this tissue to offset osteokinematic momentum and obligatory osseous directive force.  Therefore, without this contralateral arthrokinematic tension the osteokinematic directional guidance from the bone surfaces of the O and A would promote over lateral flexion, rotation, sagittal movement at some place or point in the transverse or frontal planes and possible joint subluxation.

I hope this helps in understanding the role eccentric ligament and muscle tension plays during opposite obligatory osseous directed movement.  Thanks again for inquiry.