AITAH for not supporting my wife?

My wife suddenly hates cats because she is allergic to them. She called me to tell me she is going to shoot our neighbor's cat with a bb gun if she sees it in our backyard again because it came over ONCE and made our dog bark. She wants me to go talk to the neighbors about letting their cat out. I'm not going to do that. I told her she can do it. She told me not to be surprised if she does actually shoot it. I told her it's not attractive for her to be violent and aggressive. She hung up on me and now is angry with me. She just texted: "Divorce me already then....thanks....no sweet person here.....that's what I needed to hear. Whatever!"

I'm dumbfounded.

I can't paste an image of the chat, but I posted it in another subreddit, for full context.
AIO to thinking my wife is out of line here? Help me figure out where I'm wrong : r/AmIOverreacting