Mavericks Internet Sharing Ethernet to Wifi suddenly stopped working
Try changing the password for the Internet Sharing WPA2 Personal.  I had the same problem where the Internet Sharing icon (WiFi with arrow) would flash for a moment in the menu bar, and then go back to the usual WiFi icon (signal bars.)  Resetting the settings for the Internet Sharing network fixed it.  (I was messing around with some settings files somewhere inside OS X's directory structure...so serves me right.)