Let's fix types

Ice
>now resists grass and water
(ice turns water into ice, unless its warm which requires heat anyway, and grass can't grow in snow or on ice)

For the fire, water, grass triangle, whatever the type resists, it is now immune to
(buffs all three, also it makes relative sense)

Grass
>No longer weak to flying
(never understood this, never made sense to me for flying to be good against it)

Water
>Now weak to poison
(water pollution)

Fairy
>Now weak to Psychic
(you can outsmart a fairy, its in myths and stories)

Dark
>Now supereffective against Bug
(Adds a dragon-like rivalry between the types, reason being that dark moves, like underhanded tactics like flyswatters kill bugs)

Bug
>Now resists fairy
(bugs and fairies coexist in the woods anyway, makes sense for them to resist each other being as they have a symbiotic relationship)

Fire
>now weak to flying
(When you blow hard enough on a fire it goes out)