I found this from another forum, and it solved the problem for me. At first I thought it was hardware support issue (rMB 12"), but it wasn't.
If you can't get Split Screen to work (side by side full screen windows) in El Capitan, you'll need to enable "Displays have separate spaces", located in System Preferences > Mission Control. This will require you to log out and back in. Then, simply click and hold on the green "Full Screen" button and drag the window to another part of the screen. Voila!
http://forums.imore.com/os-x-el-cap...pitan-split-screen-if-you-can-t-get-work.html
Bingo, that was the problem. Thanks for sharing it.