give this a fair shot
Three months ago, I relocated for my long-distance boyfriend. I left my dream job, my beloved city and great friends, and took a significant pay cut to move to a new city to live with him. When I first made the move, we were incredibly happy to finally be ending our long-distance relationship. Now, things are markedly different.
We've been fighting almost daily, and my usually sunny disposition has dimmed dramatically to the point where friends and family are starting to worry about me.
The main reason we fight is because of my cats — two adorable, sweet and loving cats I adopted five years ago, long before I met my boyfriend. My boyfriend has never been fond of my cats, but told me he would do his best to get along with them when I moved in with him.
He hasn't. His only interaction with them has been to yell at them and chase them into a tiny powder room where we keep their litter box. They've become so scared of him that they hide in a crate to avoid him. To make matters worse, he has a dog that he treats like a king, and expects me to do the same.
He now says he doesn't think he can live with cats, and he wants me to send them away to live with my parents. I feel like this is incredibly unfair to me and diminishes the importance of my cats in my life. If the tables were turned, I feel he would absolutely choose his dog over me.
Part of me wonders whether this goes beyond just a hatred of cats. Is he simply unwilling to compromise in general, whether it's about cats or anything else? He says that's not the case, and that without the cats, things would be back to normal. I'd love to give this a fair shot since I've already sacrificed so much and it does seem silly to end a 2 ½-year relationship over cats.
give this a fair shot はどのような意味でしょうか？よろしくお願いします
補足
ありがとうございました とてもわかりやすかったです＠