I'd prefer the word explain.
verb: explain; 3rd person present: explains; past tense: explained; past participle: explained; gerund or present participle: explaining
make (an idea, situation, or problem) clear to someone by describing it in more detail or revealing relevant facts or ideas.
It's true that the word argue does include a similar definition, but I think the #2 definition fits more appropriately with the average connotation of the word.
verb: argue; 3rd person present: argues; past tense: argued; past participle: argued; gerund or present participle: arguing
1. give reasons or cite evidence in support of an idea, action, or theory, typically with the aim of persuading others to share one's view.
"defense attorneys argue that the police lacked “probable cause” to arrest the driver"
synonyms: contend, assert, maintain, insist, hold, claim, reason, allege; More
formalaver, represent, opine
"they argued that the government was to blame"
persuade someone to do or not to do (something) by giving reasons.
"I tried to argue him out of it"
2. exchange or express diverging or opposite views, typically in a heated or angry way.
"don't argue with me"
synonyms: quarrel, disagree, squabble, bicker, fight, wrangle, dispute, feud, have words, cross swords, lock horns, be at each other's throats; informalspat
"the children are always arguing"