Everyone lives at home, that's what home means!

ok

Oh...ohhhh I got some bad news for you...

Home is where the heart is! So your real home's in your chest!

Technically true, but there are some contexts where it makes sense to say you don't live at home. Many college students live in college dormitories but still consider their parents' house to be "home"

I don't live at home, I live in a shitbox some parasite is extorting me to exist in.