Because it doesn't capture that you are eating outside your home. In fact, in the cases I can think of where you can do something "out of" a place, you're actually in that place (i.e. "working out of my office" means you're in your office working.) Think of that place as your base of operation, and you're performing the action in that location, and you have the basic idea of the context.
If I understand the Italian context right (and that's a big if), what they're saying is "I alway eat at places other than my house". In that case, in English we call that "eating out," so we would say "I'm eating out".