Share my Mac’s internet connection (WiFi) with my iPad or iPhone via Lightning cable
Check System Preferences > Network

There appears to be a problem with your network configuration. You should indeed have seen a iPhone USB item in that list of “Ports”.

Check your System Preferences > Network settings. On the left you should see an item for the network interface name something like “iPhone USB”. If not, try using the Location popup menu at top to Edit Locations and add a new location. Alternatively, you might try the + icon button to add an interface of that type to that list.



Now go back to your System Preferences > Sharing > Internet Sharing where you should now see an item named something like iPhone USB. 



From there, turn on the Internet Sharing checkbox to start sharing. If it does not work, try rebooting your iPhone (hold down Power/Sleep button).

You can test to be certain by turning off your iPhone’s Wi-Fi, Bluetooth, and Cellular Data. If you have internet access, then you must be using the USB cable connection to access the internet over your Mac’s Wi-Fi connection.