A typical person would be insulted if you claimed that their moral statements referred only to feelings. Most philosophical definitions work on a principle which isn't quite like how ordinary people see them but would seem close enough to an ordinary person.

There are a lot of uses of the concepts of right and wrong, not just people arguing with each other. Ethical dilemnas, people wondering whether to do the "right" thing or the "wrong" thing, philosophical schools (think of the Confucians, for example, who don't define 'right' or 'wrong' but talk about it a lot). Your conception only covers one use.