Why can’t I share my Internet connection with another Mac? I tried to share my Internet connection with another Mac but it failed. I could before I upgraded to Mountain Lion.

I have a 3G USB modem that I use for Internet. I went to System Preferences → Sharing → Internet Sharing → Select my 3G device from Share your connection from → Tick WI-FI → Setup WI-FI Options... and then enable Internet sharing.

However, the other Mac can see my network but cannot join.

How do I fix this?

HW: MacBook Pro Retina 15"
OS: Mountain Lion
You could try disabling your Wi-Fi, changing the sharing settings so that the security is off (just for testing purposes of course) then enabling your Wi-Fi and try again.