Golduck is not a Psychic type because of the brain damage it had as a Psyduck.
Floette is not a Grass type because it only holds a flower, same with Flabébé. Florges is weird, it is a flower. But she is still not a Grass type because: "Its life can span several hundred years. It’s said to devote its entire life to protecting gardens."
Fae are usually associated with Nature, protecting it, and making it grow. Which she both does. So basically, in this case the Fairy type replaces both the Fairy type and the Grass type. If the Fairy type didn't exist, then Florges would just be Grass. Cottonee for example is both Grass and Fairy type, because these Pokémon are pranksters, and leave cotton behind, resembling the mist fairies like Tinkerbell leave behind.
Eelektross is not a Water type because if you are a fish/other sea creature, you don't always need to be Water type. Take for example Dragalge, it got the Dragon type instead of Water because Dragon fits it more.
Gyarados Is based on a sea serpent and chinese dragon, but it has more reasoning to be the Flying type because: "Gyarados is partially based on a legend about how carp that leapt over the Dragon Gate would become dragons. Several waterfalls and cataracts in China are believed to be the location of the Dragon Gate."
The jumping was pretty high, so the flying type was a reference to the jumping.
And also: "s Flying-type may be a reference of koinobori, a carp-shaped wind sock traditionally flown to celebrate the Children's Day in Japan. It could also be inspired by the Inkanyamba, a giant, winged, eel that causes storms when angry - a trait Gyarados is famous for."
(sauce)
Lugia is not a Water type because water has something in common with the moon. This is because of tides. And the moon usually resembles magic, and magic resembles Psychic. Therefore, some people think that Ho-Oh and Lugia are supposed to be representing the sun and moon, before Solgaleo and Lunala did. So again, the moon resembles magic, and magic resembles the Psychic type. Lugia is also the Psychic type because Morimoto Shigeki said: "To start, the first type was decided to be Flying-type since Lugia have wings. At the time Psychic-type was the symbol of powerful Pokemon. As we wanted Lugia to give the impression of being a powerful Pokemon, we settled on Psychic-type for the second type, instead of Water-type.
In short, the reason why Lugia is not a Water-type despite being underwater, is due to its Flying-type-like appearance, and Psychic-type being the symbol of a powerful Pokemon."
TL;DR:
- Golduck is not a Psychic-Type because of the brain damage it had as a Psyduck
- Floette and Flabébé are not Grass-Type because they only hold flowers. Florges is not a Grass type because in this case the Fairy-Type replaces both the Fairy-Type and the Grass-Type
- Eelektross is not a Water-Type because the Water-Type is just an extra type for sea-based Pokémon. If 2 other types fit better, than the Water-Type goes away
- Gyarados is not the Dragon-Type for the sake of rarity (but a reward would be nice....), and because it is about a myth about carp that leapt over the Dragon Gate would become dragons. Referencing the Flying type because it was pretty damn high.
And also the Koinobori, a carp wind sock flown to celebrate a day. also the Inkanyamba a winged eel that causes storms when angry
- Lugia is not a Water-Type because water has something in common with the moon (tides), and the moon usually has a resemblance of magic, magic resembles Psychic. Also people think that Ho-Oh and Lugia are supposed to represent the sun and moon (respectively). Lastly, the Psychic type was a symbol of strong Pokémon