Given that eel is clearly a water animal, one would think that it would fall under the general ruling of the hadith wherein the sea's water is pure and its dead is permissible. However, I clearly recall reading from various sources that eel is considered haram by at least one of the major schools of jurisprudence.
The internet being what it is, I've had trouble finding reliable references thereof; the best I've learned is that eel is clearly halal according to the Hanafi school (which I find interesting, considering how many other species of seafood they don't deem thus), but I've found little more than vague references that either the Maliki or Hanbali schools consider it haram, but with nothing to back them up.
I've also not found any clear evidences as to why eel is considered thus. A few possibilities I've seen presented, again without any reliable references to back them up, are as follow:
So the question lies thus: Which school(s), if any, do not consider eel inherently halal (like other seafood), and why not?