Already filed a bug in Apple's bug reporter, ID is 25949722
What I want to do is to set Canary as default browser, but when I opened system preferences, I cannot see any browsers listed.
What's wrong with my Mac (OS X 10.11.4 - El Capitan)?
Do you have Google Chrome (I hope so since Canary is a pre-dev Chrome release and prone to crashing)?.
Go into the Chrome settings page by typing
chrome://settings and setting Chrome as the default browser (it's under the "General" tab). Once you do that, it should fix the problem you are seeing in System Preferences
It looks like you may need to rebuild the Launch Services database, which is what the Mac uses for its "what apps can open this type of file" structure.
You can either do it in Terminal, using
/System/Library/Frameworks/CoreServices.framework/Frameworks/LaunchServices.framework/Support/lsregister -kill -r -domain local -domain system -domain user ; killall Dock
Or Onyx (freeware) can do it for you - Maintenance tab > Rebuilding - check just the first box & execute.
I deleted the Opera browser and it solved the problem.