Why do I pretend act so tough in public? How can I break this habit?

Honestly, it seems that you have given yourself a pretty good self-estimate. My recommendation would be to seek a counselor that can help you overcome your issues (which seem to be that you overcompensate an insecurity issue in public by appearing aggressive or "tough"). Since you are conscious and self-aware of your actions, the next logical step is to seek some guidance in behavior modification. Good luck.