Why can't I edit a contact?

If you are unable to edit a contact on your account, it is most likely that you are using a sub-account and this is a shared contact, which was created under the parent account and shared to your account. 

Shared contacts are identified via a small "share" icon next to the number:

In order to edit this contact, you will need to either do so via the parent account, or export the contact from the parent account, and then import it directly into the sub-account (making this a new contact that is native to the sub-account)