I honestly can't imagine why anyone would let anything that happens on a site like this bother them personally. Is there something I'm missing?

Sometimes people are just easily offended. And it's a wee bit silly.
But also, people are people, online or off. You're still interacting with another human (assuming they're not really a bot 🙄) even if you can't see them. A lot of the same stuff in regards to getting annoyed or being offended apply.