It has to go both ways, which is why F/G/W is different
Fire is strong against Grass is strong against Water is strong against Fire.
Fire resists Grass resists Water resists Fire.
Dark/Ghost/Psychic works one way, but not the other, as Dark is immune to Psychic. There are a few that work both ways that aren't Fire/Water/Grass though:
Flying would have to have a double type because of how Flying-types work, which would mess up the starter triangle, and Steel as a starter isn't viable since it's so OP with resistances. I would guess with the last one that they wouldn't want a starter with an immunity maybe? Like Ground?