Because there is nothing wrong with it

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What are otherkin?
People in a human body who identify/feels very connected to something. Whether it's religion or plain identification. Usually passed down from the creature's soul into their body, really comes down to culture. It does not always have to be an animal, supernatural beings, time traveling humans and plants count

Oh, those! They're disgusting and idiotic! Wolfaboos everywhere
Those aren't real otherkin those are fakers who give otherkin a bad name. Those people obsess over animals and pretend to be them. 

They're annoying and mentally ill!
Oh so you're going to use that as an excuse to harass and attack them? Congratulations, you're an ableist scumbag who uses one's 'mental illness' as an excuse to harass and bully them.

Delusional little shits! Just want to be their favorite animal!
They aren't delusional at all, they know they are physically human, and if they deny it, that's there choice and the don't always identify their favorite animal, there is no choice.

They shove their otherkin-ness down my throat!
No they don't, if they correct you for something fucking correct yourself instead of making it about you.

Stupid pronouns they come up with! They're not even part of any language! Their pronouns make other pronouns hard to take seriously!
News flash, all words were made by some person at one point. Shakespeare made up so many words that we use everyday(assassin, swag, etc)
Yet we don't look down on him for his words. Call them what they're comfortable with and get over it, they never questioned your pronouns. 

They're all furries!
Furries are anthromorphic animals that are cartoon characters and furries themselves admit to not being their fursona. 
Some otherkin are furries, furries are not otherkin. 

They're annoying shit and plain stupid! They should accept what skin they were born as !
Accept that you're annoying
Ask yourself this, does somebody being otherkin-
Negatively affect you
Can harm you
Be considered a direct insult to you
Because they aren't. They're living their life just like everybody else and if you look at that one harmless trait and find it good enough to attack them for, than please teach yourself how to tolerate. They are harmless, unlike your xenophobic behavior. 
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Get over the fact that not everyone is going to identify as a human because that doesn't affect you anyways. Try to live a day without disrespecting one's existence and learn to accept.