My wife has been like this for as long as I've known her. She hates spiders, even if she rationally understands they aren't a threat and are good for eating other bugs.
But now she's passed her fear on to the kids. And I'm not always around to slay the demons, so she goes full mama bear and destroys entire rooms to swat a daddy longlegs.
Our son is 11 now and as tall as she is, and is generally well-adjusted right up until he sees a cobweb on the ceiling during a shower and starts screaming like, well, exactly like my wife does. And she has to be the adult and tell him he's overreacting, and that there's nothing there that can harm him.
And our daughter, 9, is not happy to see a spider, but hates killing them more than she hates seeing them. So she's screaming, too, saying "Don't kill it, what if it has babies and they miss their mama!"
So I was out at the store, and come home to my son, soaking wet and wearing only a towel, cowering behind my wife, who has ripped the shower curtain rod from the wall and is wielding it like a sword, and my daughter begging them both to let it live, saying we can just move to another house and let the cobweb have this one.
Yes, I said cobweb. Not even a spider. Just where a spider was once.
So that's how our first day of school has gone so far. How about you?