I’ve had a few issues trying to change the default mail client on El Cap. In nearly every case, after changing it in Mail (seemingly the only place you can actually change it), the change doesn’t stick. After quitting and relaunching Mail, it’s back to the default of Mail.app.

I’ve found that if you clear the Launch Services database, this may allow the change to persist.

So, quit all running apps.

Open Terminal and enter in the following (all on one line)

/System/Library/Frameworks/CoreServices.framework
/Versions/A/Frameworks/LaunchServices.framework
/Versions/A/Support/lsregister -kill -r -all local,system,user

When it returns, you can quit Terminal.

Launch Mail, go into Preferences > General and set the Default email reader to Microsoft Outlook

Quit Mail and the change should stick.