Despite being a carnivore, the diet of the bear is largely

IMO,
A would have been correct had it been "and rarely animal carcasses".
B is very disjoint from the rest of the sentense.
C is very obviously wrong.
D misses "with" to join with the remainder of the sentense.
E is quite correct, though a simpler formation would have been a modified A "and rarely animal carcasses".

So I'd go with E.

Should be E since "with" is needed to use the term "rarity" most appropriate

This is a surprisingly tricky sentence, and to really understand it you must understand that it involves elliptical construction: a couple of key words are implied, not explicity written in the sentence.

It may help to see the "true" sentence with the ellipsed words:
Despite being a carnivore, the diet of the bear is largely vegetarian [, including] fresh leaves, fruits, berries, nuts, roots, and tubers, with animal carcasses [as] a rarity
(that's how I'd view the sentence, others could assume something slightly different but the principle is the same)

Here, including is a "present participle" -- a verb ending in -ing that is operating as an adjective. The whole phrase "including fresh leaves, fruits, etc" is an adjective phrase, modifying diet. It is a nice bit of style to, instead of actually using the word "including", set that group of words off with dashes.

It helps to know that, so that now you can simplify the sentence. Remove the adjectives and adjective phrases in the first part of it, and you have:

The diet is vegetarian, with animal carcases a rarity.

Hopefully you'll see that THAT choice sounds much better than the alternatives, which are all at least a little bit wrong.

Finally, you should know that your sentence as written suffers a favorite GMAT error. "Despite being a carnivore," should be followed by the word it modifies -- "bear", not "the diet".

Very good Explaination,super cat

OA is E