Okay so those are 2 different things you described:

“At least we aren’t Ohio!” - this is a common phrase for pretty much any obscure/lesser known states. I wouldn’t count this as hate towards Ohio specifically. I hear plenty of times “at least we’re not in Kansas” etc. shit like that.

As for the Ohioans who say, “I hate this place! I can’t wait to move away” - yeah that’s normal for every state. Everyone craves exploring new places and come to resent the place they grow up and they usually all end up missing it sooner or later too.

So to answer your question, it’s because we’re lesser known. Of course people from California or whatever are going to talk down on places like Ohio. That’s always been a thing.