How to identify permissions which current user lacks to access node create page?
Devel Node Access (DNA) provides detailed information on permissions that take effect. 


  View the node access entries for the node(s) that are shown on a page. Essential for developers of node access modules and useful for site admins in debugging problems with those modules.


Unless some modules abuse access system with dirty hacks, it should pretty reliably identify which module refused access to given user.