Am I the asshole?

I have a cat. I got her a year ago and prior to this I did not like cats (misinformation about them) but they are amazing animals and I adore them now.
My sister has a one year old and she’s struggled to find a nanny and now she has a job offer so she has to get one fast and she asked me to help her son adjust to the nanny because his antisocial and takes time to accept new people. So I agreed to help out for a month assuming by then he would’ve adjusted and if he doesn’t that’s none of my business I have my own life to live. So now she’s saying I should leave my cat alone at home and just give her enough food for that time and I refused because that’s my baby why should I? And she goes on to say I’m imposing the cat on her and I said I’m not, I’ve told you I have to come with her if you don’t like that that’s fine find someone else for that month.
So now she’s saying I’m choosing my cat over her and her sons ( I love them all to death her sons are practically my kids) and I didn’t love cats before and it’s just an animal and they are human beings. I’ll have children one day I’ll probably stop loving the cat ( 😂what kind of dumb logic is that) and when I’ve gone to her house with my cat before there was fur everywhere. So I told her you’re not welcoming of my cat and so I won’t also babysit or anything because that requires me abandoning her for your needs and that won’t happen I got her because I wanted to love her and not just for aesthetics.
So, am I being unreasonable?
Am I the asshole?
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