1. Debate Ideas and Rules

Definition of Argument:

1. To put forth reasons for or against; debate.
2. To prove or attempt to prove by reasoning.
3. To give evidence of your reasoning.
4. To persuade or influence, as by presenting reasons.

Synonyms of Argument:

Argue, quarrel, wrangle, squabble, haggle, and bicker.

These verbs are compared as they mean to dispute.

Argue This implies intent to persuade an adversary in debate.
Quarrel This stresses animosity and estrangement.
Wrangle This refers to loud, contentious argument and squabble to minor argument over a petty or trivial matter.
Haggle This specifies verbal bargaining usually over a price, in a petty way.
Bicker This suggests sharp, recurrent exchange of remarks on a mean or petty level.

You need to be very polite when disagreeing with someone in English, even someone you know quite well.
With someone you know very well, you can disagree more directly.