Hi Ken,
The quick answer is Fusion 360 doesn't support opening files locally. You need to be online to upload your file. Then, once you open it you will have the file available.for offline use.
As Fusion 360 is a cloud based tool, it does not support local file opening or file storage. The process of getting files opened in Fusion is done through uploading. Offline mode is used as a means to continue work on files previously synced with your Fusion account when connectivity is disrupted (like if your internet connection is patchy or non-existent on an airplane or something like that). Once you upload the file, open it on your machine and then that file will be stored in your temp drive. You'll be able to work on that file in offline mode. Note: the default time to save files in offline mode is two weeks. If you need to extend that period, that option is available in your user preferences.
Here is a broader article that speaks more to how Fusion handles importing, exporting and sharing in general:
Cannot Open Local Files in Fusion 360
Hope that helps,
Mike
Michael Aubry
Autodesk Fusion 360 Evangelist