It's an Integrated feature for Animal Crossing New Horizons: One save game per Switch. If anybody in your household would love to Animal Crossing Bells perform their particular island and enjoy the Island President therapy, wellthey will need to obtain a completely new Switch system and a new Animal Crossing game.
Otherwise, all non-first profile to initiate a match in ACNH are second class citizens residing in someone's island and are barred from progressing the sport or taking any meaningful decisions in its development.
You would be surprised how many ACNH earnings are in fact just people buying another copy so that they may have a second island on a second Switch and play them both at the same time (some people use the secondary island for storage, or simply to become creative in a way they are not on the main island).
Trading things or visiting another island to buy Animal Crossing Items drop or pick up things can only happen when both players are online, so yes, you need two copies of this game on two different systems running at precisely the same time.