When it comes to English, abandon logic. That's my motto.
Everyone needs to throw up their arms in disgust.
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The plural possessive pronoun 'their' refers back to the singular subject 'everyone' ... hey, wait a minute! Shouldn't everyone be plural? It refers to many people, right? Everyone here thinks so. Rats! There we go again, writing the verb as if the subject 'everyone' were singular. What a singular thing that is! That it's singular, I mean.
)