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“What’s so great about Hexbear? Why do people keep talking about Hexbear? What’s so special about this instance?”
(hexbear.net)
Maybe it is more than an instance. Maybe it is an idea, a world-historical vanguard, light itself. 
actual attempt to answer (cringe)
We’ve been around for three years on a lemmy fork before federation. The lack of federation for years as well as the place we splintered off from (/r/chapotraphouse) already having a unique microculture within Reddit has given this instance, in my opinion, a distinct culture compared to general-purpose and even other hobbyist instances.
Regarding specifics, Hexbear is a vehemently queer-friendly/intersectional anti-sectarian socialist instance. Check us out 
And it's very much appreciated from the otherkin community. When you live as a nonhuman, you become acutely aware of the fact that 95% of people are human supremacists and think your life isn't worth protecting because you're an "inferior species". Cue the old "if they want to identify as animals they should be eaten like animals". Carnists are fascists and this is the rare non fascist community.