Pat the pork shoulder dry with kitchen paper, making sure it's cut into at least 2 pieces (to help it fit into the Instant Pot better). Set the pork aside.
Combine the dry rub ingredients in a bowl, making sure everything is well combined.
Rub the dry rub onto the pork in an even layer, covering every side.
Heat up the instant pot on "Saute" mode and add the oil. Brown the pieces of pork shoulder on all sides.
Add all the pork pieces to the Instant Pot, add the Root Beer (or cola), Worcestershire sauce, and water (or stock).
Add and seal the lid, turning the valve to "Sealing". Set to "Pressure Cook" for 60 minutes.
When the Pressure Cook time is finished, carefully turn the release valve to "venting" using a long pair of tongs or another long kitchen tool so you don't burn your hand, arm or face. It's a good idea to do this under an exhaust fan in your kitchen, if you have one.
Remove the pork to a bowl and shred it, adding the barbecue sauce (try my homemade Honey Garlic Barbecue Sauce) and some of the cooking liquid (if needed, to loosen it up). Discard the rest of the cooking liquid.