Looking at this, I wonder what's the oddest couple you could make between the Ship Girls.
When I first knew about Kancolle, I could only recognize Kongou and Shimakaze who appeared on almost every pages I saw about the game, so I am curious to the "abnormal" relationship between them.
Because, if you read Kagerou's lines closely, you see that she is insecure. Kagerou's worldview is focused around what she sees as her duty ("expect great things", "out of a textbook", "not fit to be the nameship...") and the expectations placed on her. Kagerou class is supposed to be the perfection of Japanese destroyer design, after all, and came into commission during a dark time for Japan.
But Fubuki's worldview is entirely different. She's the genki, ganbaru special destroyer that shocked the world. Since she is even the main character, reality bends around her wishes. At the time of her commissioning no one expected anything of Japan, and there was no China affair or any looming conflict with the US. All roses for her, and her lines and character all all appropriately full of hope for the future.
The animosity Kagerou feels for Fubuki is probably akin to that of a young man who is unable to get out of his father's shadow.