This issue is fixed in version 15.0.4841.1001 or later. Click File, Office Account, Update Options, and then click Update Now to update to a newer version.
Outlook 2013's Mail applet will not open from the Control Panel following the June 2016 updates. Click-to-run installations are affected on all operating systems. When users click on the Mail applet the mouse cursor circles, then stops without the applet opening. Right clicking and choosing Open, or using the Run dialog to open the applet also fail.
This problem affects users who install the June 2016 update for Office 2013 Click-to-Run, version number 15.0.4833.1001, or a later version.
Most Office 2013 users will have a click to run version of Office 2013 installed, including all subscription installations. To verify your version information, click File, Office Account in Outlook (File, Account in other Office applications.) Then click About Outlook (or About [application]).
Microsoft is investigating this issue and until it is fixed, users who need to create a new profile or open a different profile can either open Outlook using the /profiles switch or set a registry key to always display the Choose Profile dialog. Click the New button to create a new profile.
To use the /profiles switch when you open Outlook, open the Run command using Windows key + R then type or paste Outlook.exe /profiles into the Open field and click Ok.
The option to always prompt for a profile when starting Outlook is stored in the registry. To add or change the value, open the registry editor and browse to and change the PickLogonProfile value. If PickLogonProfile does not exist, you'll need to add it.
Value: 1 = Prompt for a profile to be used; 0 = Always use this profile
If you don't want to edit the registry yourself, you can download and run this registry file.