The same as how a bird can be scared on snakes. Interestingly native birds in Australia aren’t scared of humans.
I don't have fear of spiders (was surprised by how many people do fear spiders). When I was young, I "hosted" a bunch of them under my table. Thinking of it, I think most people have their fears transmitted through their mothers. My mom certainly didn't fear spiders but she hated their "dirty" webs.
For example I do have a strong reaction to cockroaches till this day; a harmless insect that my mother fear. I can't even look at the beast. My cousin do not and conversely do fear spiders.