I am guessing that because you are using a USB internet connection, that
Sharing thinks you are getting your internet via your ethernet device, so it does not include that device in the list.
My Verizon DSL modem comes with an ethernet port (It might have USB, but I ignore that). I then have that ethernet port plugged into a home WiFi base station which then redistributes my internet connection to all the other systems in my home.
If you have an ethernet option from your Verizon provided broadband modem, then the simple and robust solution is to get an inexpensive home WiFi base station and use that as your home router for your Mac as well as your Xbox.
Now if you want to continue to play with using your Mac as a router, then start with System Preferences -> Network, and see if you have a "Built-in Ethernet"?
Does the fine print under the "Built-in Ethernet" say "Inactive"? If it does then this port has been explicitly disabled. Use the little Gear icon at the bottom of that column and select "Make Service Active".
If you have a "Built-in Ethernet" and it is
NOT "Inactive", then you could try duplicating it via the Gear icon at the bottom of the column. Maybe that will give you an Ethernet sharing option.
But again, your life would be so much easier if you put a home router between you and your Verizon internet connection. Besides a home router is also a hardware firewall that does not allow internet bad guys into your home network.