To make a change to a process (workflow) in CRM you need to be logged in as the owner of the process. If you are not the owner and you try to make a change, you get the following error: The Process cannot be published or unpublished by someone who is not its owner.
How to resolve this error message:
To remedy this, select the process, click the assign button, and change the owner to you.
Now, you can update and activate / deactivate the process. When you're done, you can reassign it back or keep ownership, whatever makes more sense.
TECHNICAL NOTE: This same principle applies during import of a solution, if the solution has an updated version of a workflow in it, the person importing the solution must be the owner of the workflow in the CRM system or it will fail.