Unicorns are John Green's most hated animal for a few of reasons.

• They refuse to disarm, stubbornly retaining their horns, which John references as "[a] deadly weapon afixed to my face"
• Their blood is restorative, the result of which is that Voldemort is able to kill many promising young wizards who no doubt would have gone on to decrease major worldsuck

A brief history:
        
During John Green's time in the Netherlands, he recieved an invitation to dinner and, having to use Google Translate, discovered that the final sentence said, "We do not know which of [the guests] will eat the unicorn." John then proceeded to volunteer on the grounds that unicorn blood is restorative.
       
In a Question Tuesday video, John Green was asked his opinion on Scotland's national animal. He proceeded to say he loved bagpipes and when informed that bagpipes weren't animals, asked what the numerous "holes and pointy things" were for. He was outraged to discover that Scotland's national animal is the unicorn.
       
Most recently, John Green was nearly tricked into saying "I love unicorns" during a recent video. Luckily, he stopped himself before finishing the sentence, thus saving the world from being overrun by decepticons and destroyed in the greatest worldsuck event in history.