Sometimes Outlook 2016 will just hang in some state, such as "processing" but not opening, or "send/receive" but never connect. The following fix often will work:
1) Click the Windows button or press the Windows key on your keyboard
2) In the Run box, type outlook.exe /safe [Note: there's a space between "exe" and the slash]
3) Click OK
4) When prompted to ‘Choose a Profile’, click OK (you may need to choose a profile if you have multiple ones)
5) Outlook will open and it appears to repair itself
6) You can exit Outlook and restart it normally to verify that the fix worked, although some of your view settings might have changed.