[RejZoR]

Cannot use OFFLINE mode when your internet connection is down?
Offline Mode refuses to activate in such scenario? This usually only happens if you're using wireless or wired router. Make sure you disable the connection by unplugging the cable from PC or disabling connection through Windows settings. If you don't, Steam will think it's actually connected, but when it will try to go into Offline Mode, it will fail because connection doesn't actually exist (it sees the router link).

When you disconnect the computer from connection, use Offline Mode again and it should switch.
I was banging my head against wall because of this when my ISP link dropped off the Earth for 3 days and i couldn't play a single Steam game. Then i found out it was router's fault to fail like this...