I have a user that is using Outlook/Exchange 2010 on a Windows 7 box and his Share Calendar option is greyed out.  All other users are able to share their calendars.

Hi,

Please test in Outlook Safe Mode:

Press Win + R and type outlook.exe /safe in the blank box, then press Enter.
If theres no problem in Safe Mode, disable the suspicious add-ins to verify which add-ins caused this issue.

Please make sure inheritance is checked under the security properties of the user (in AD).

Also check full permission given on that mailbox to 'Self'.

Regards.

Melon Chen
TechNet Community Support