There is a difference between being assertive and being aggressive.
Assertive means you are confident in both body language (good posture, stance, and comfortable hand movements) and delivery (tone, pacing, and volume are controlled and organization is clear).
Assertive means you speak with conviction that you believe the argument you are presenting.
Aggressive means you go beyond confidence to confrontational.
Your body language will be distracting because it is too big and showy or perhaps you position yourself in a fighting stance towards your opponent.
Your speech will be too loud, too boisterous, and attack your opponents rather than their arguments.
There is never a round where you should be unprofessional. Swearing, yelling, personal attacks, biting sarcasm, and aggressive hand movements do not belong in a debate round. You would never think of a business executive yelling at a client he or she wanted to win over.
Being assertive means you have the confidence that your argument speaks for itself and is persuasive. Aggressive debaters seem to make up for a lack of confidence in their argument with their confrontational words and actions.
Assertive debaters are polished and professional. Aggressive debaters are dramatic and bully-like.
Assertive debaters are focused on winning their arguments. Aggressive debaters are focused on beating their opponents.