Jamal,
I am assuming that you are using a sde 10.0 geodatabase or one prior to that, because in a sde 10.1 geodatabase we can separately grant Insert, Update or Delete privileges. From the images, it shows that you are using ArcGIS Desktop 10.1 but the version of the sde geodatabase will still matter.
Still just FYI, you can grant Insert, Update or Delete separately from 10.1 onwards. Here is a snap showing that:
[ATTACH=CONFIG]21277[/ATTACH]
Hope this helps.
Regards,