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These are people, their entire personality is defined by their "thing". When someone says "anime sucks", the anime poster doesn't see it as someone expressing an opinion, they see it as a direct attack on themselves. You see this a lot with sports teams, car brands, etc. Anime posters have an average IQ, and are completely un-noteworthy. They probably have little accomplishment or achievement in their lives. As a result, they need something external to themselves to define their identity.
When you attack anime, you are directly attacking their very core, the essence of their being. They absolutely must come to it's defense, and attack you personally in return.