I think there may be some misunderstandings here
- "Sharkbite" is both a brand name AND a trademark for a type of solderless fitting-to-pipe connection. The connection type came first and fittings using it were branded as "Sharkbite" by the company. They have now branched out into also selling fittings with traditional types of connections (threaded, soldered, etc) and these are also confusingly branded as "Sharkbite".
I believe the OP may have a Sharkbite brand fitting with traditional non-Sharkbite connections. I believe the experts here are referring only to the Sharkbite connection style.
- Traditional 3/8" compression connectors are typical for the outflow from a faucet supply shutoff valve to supply lines running to a faucet.
If the faucet supply line is (semi-) rigid copper/brass with no connector on its end, the ferrule and nut are necessary to clamp and seal the line in the compression connector. The nut compresses the soft metal ferrule into the line and fitting, making a watertight seal. Such rigid connecting lines were common for faucets 50-100 years ago.
In modern US residential sinks, flexible braided faucet supply lines are normally used instead. To maintain compatibility, the braided supply line connector ends thread onto the same male threads of the compression connector in place of the ferrule and nut. They have end connectors that only need to be tightened hand-tight plus maybe 1/4 turn more to make a good seal, because of a rubber seal inside.
I think the OP is connecting such a braided supply line to a compression connector on the shutoff valve and so should NOT use the ferrule and nut shown, as the braided supply line's connector takes their place.