Sarah probably thinks that Irma is either mocking her, or thinks that Irma considers it a toy or something that can just be picked up and played with, which is affronting to her mind.

Irving probably thinks that Sarah is being judgemental or having double-standards; if she can become a girl, why can't they be both a boy and a girl?

I can get why they are both feeling a little touchy on this issue - after all, being transgender is the core thing that defines Sarah's personality. She's desperate for someone else her own age that she can share things with. Meanwhile, Irma considers gender to be something that shouldn't be restricted to what's in your knickers, so they want to be able to choose how they present in the world on a day-to-day basis, depending on how they feel. I think overall, I'd probably stay out of siding with someone here.

-- Noelle (I'm delightfully intersex :P)