To explain this in an easy way, you need to understand the primary function of a fin.
The primary function of a fin is to prevent the board from moving sideways, i.e. giving it a direction of movement, i.e. giving it grip on the water.
Now, for the same course, the same sail size, the same wind force, the same weight of the rider, the wider board needs a bigger fin than the narrower board, simply because the weight of the rider is devided over a larger surface, hence less downward force per surface area, hence less grip of the board, hence more grip & steering action needed from the fin, hence a larger fin.
Extremely put, if a board would be as narrow as a blade of a knife, it would not need a fin at all.
But it would also sink