In Harry Potter each house has its own animal that represents it; is it ever explained how these animals came to represent a specific house? I never read a canon explanation to who chose the animals, is that known?
Since the four founders were involved in choosing students for their houses, it seems reasonable to assume that they also chose their house animal.
Reading the welcome letters on Pottermore offers one explanation: the animals were chosen because they had the traits that the founders valued in their students.
Somebody who knows more about history than me might be able to comment on thehistorical significance of these symbols in medieval times (when these animals would have been chosen).
2 of the 4 are pretty obvious:
Salazar Slytherin was a Parselmouth, therefore very close to snakes, which immediatly leads to the snake as a symbol.
To be in Gryffindor one has to be brave beyond any other personal quality, what animal stands for courage? Exactly: The lion.
As far as the other to houses are concerned:
I think from wise to eagle is not that far a fetch, I also consider this to be pretty obvious.
The badger is known for having a gentle nature and has come to be the symbol of love and loyalty; both are traits of Hufflepuff house. It also is an ordinary animal if there is any, If there is a more specific reason out there I have not seen it yet
While this may not be what J. K. Rowling intended originally, this is what the badger symbolizes and its character traits. Note that she originally considered the bear as the symbol so these traits would connect. What was Helga Hufflepuff’s animal ‘avatar’?
The badger symbolism shows how the badger is actually regarded and also how Hufflepuff can bring out the best traits in a student. Even the mountain lion will hesitate to take on a badger and it shows that "size" can be irrelevant in defending what is yours.