The Kremlings were cold-blooded reptiles, which are usually carnivores. Why would they go to the immense trouble of stealing the Kong banana hoard and defending it from our two favourite monkeys on cold turkey?
From the Donkey Kong Country manual for the SNES, emphasis added:
... Donkey Kong had assigned Diddy to guard duty on this awful night, and he was not happy about his fate.
Donkey Kong's earlier pep talk kept creeping back into Diddy's mind. "OK, little buddy," Donkey had said in his patronizing voice. "As part of your hero training, you've got to stand guard tonight over my bananas... I'll relieve you at midnight, so try and stay awake until then!"
Buddy? Yeah, right. Now he was alone [sic]Alone unless you counted the unknown threats which lurked behind every tree that he glimpsed during the lightning flashes. The Kremlings were out there, this much was certain. They coveted Donkey Kong's banana stock-pile, the largest on the island, and probably in the world. A treasure in potassium and Vitamin A. The perfect food. "Ahhh... delicious bananas..."
In spite of being reptiles, the Kremlings wanted DK's bananas because they are the "perfect food." This is probably from the perspective of the Kongs, its more likely that the Kremlings stole the bananas because DK valued them so much -- he stores them like money or treasure in a cave. Perishable bananas. In a big pile. You even collect them like the gold coins from that other popular platform game...
You know he's serious about these bananas because he vows to retrieve every single banana (even though in reality they would be inedible after a week or so):
Donkey Kong stood there in stunned disbelief and hadn't heard most of what Cranky said. "Diddy... gone... My little buddy..." he murmured to himself.
Donkey Kong was suddenly filled with conviction. "The Kremlings will pay!" he raged. "I'll hunt them down through every corner of my island, until I have every last banana from my horde back!!"
Then Cranky Kong calls out the absurdity of retrieving stolen bananas as a video game plot:
"Find your little buddy and retrieve a bunch of bananas?!" Cranky snorted. "What kind of game idea is that?! Where's the screaming damsel in distress?!"
So they acknowledge the premiss is flimsy, but hot damn! The graphics and gameplay were awesome! So what if a bunch of reptiles stole the bananas? The point is we need retribution -- get those bananas (and Diddy Kong) back!
I can't find any official reason; Wikipedia and the Super Mario Wiki both state the reason is unknown. I would guess it's simply because King K. Rool is mean (his name is a play on the word "cruel" after all). He likes to kidnap Kongs, steal bananas, torment his minions, and destroy the environment just because.