debate，argue，quarrel 最明显的区别是quarrel指人际关系不和、埋怨乃至吵架，而debate，argue，debate倾向于比较特殊和正式的场合的争辩如立法机构，argue则倾向于一般的辩论而且往往还要提出反对和坚持的理由。细微的区别比较请看下面
debate [di'beit]
vt. 辩论，争论，讨论
vi. 辩论，争论，讨论
n. 辩论；辩论会
vi.
1. (尤指在立法机构或集会上)辩论，争论；讨论：例句: When I left, the men were still debating.
我离开时，那些人仍在辩论。I debated with John upon(或about) the question.
我和约翰辩论这个问题。2. 参加辩论比赛；参加辩论会3. 仔细考虑,思考,盘算(with oneself或in one's own mind):例句: I debated with myself whether to tell her the truth or not.
我盘算着是否把真相告诉她。I'm just debating whether to go or stay.
我正在考虑去留问题。4. [古语]斗争；争吵
vt.
1. (如在立法机构或集会上)辩论，争论，讨论(问题)：例句: They debated the matter of free will.
他们辩论过自由意志的问题。2. 争论(一个问题)，争执，对…不同意：例句: The homeowners debated the value of a road on the island.
房东们争论岛上一条道路的价值。3. 与(某人或团体)辩论(或争论，讨论)：例句: Jack will debate Jones. Smith will debate Mary.
杰克将与琼斯辩论。史密斯将与玛丽辩论。4. 思考,考虑,盘算,细想(with oneself或in one's own mind):例句: She debated her decision in the matter.
她对此事仔细考虑后做出决定。I debated the idea in my mind until I fell asleep.
我入睡前脑子里一直在考虑这个主意。5. [古语]为…斗争；竞争；争夺
近义词:
discuss .
短语
1. beyond debate无疑义，无可争辩2. open the debate在辩论时首先发言
argue ['ɑɡju:]
vi. 争论，辩论；提出理由
vt. 辩论，争论；说服；证明
vi.
1. 提出(或提供)理由(赞成或反对某事)，表示赞成(或反对)的意见，为赞成(或反对)而辩论(与for或against连用)：例句: He argued in favour of capital punishment.
他提出理由赞成严惩。to argue for(或against) a proposed law
辩论赞成(或反对)某法律草案2. 争辩，争论；争吵，争执；持异议：例句: The senator argued with the President about the new tax bill.
参议员与总统为新税法案争辩。
vt.
1. 辩论；争论；讨论；议论；提出赞成(或反对)的理由：例句: The lawyers argued the case.
律师们辩论这案件。2. 用辩论(企图)证明，论证；坚持；(坚决)主张，认为：例句: to argue that the news report must be wrong
论证此项新闻报道必定错误3. 提供…证据；证明；表明(原因等)；表示；意指：例句: His manners argue a good upbringing.
他的举止表明受过良好教育。His clothes argue poverty.
他的衣衫表明贫穷。4. 说明,劝告(into或 out of)：例句: to argue someone out of a plan
说服某人不作计划5. [1275 ～ 1325]
近义词:
discuss .
短语
1. argue in a circle用循环论证来辩论；辩论不出结果2. argue someone into(或 out of)(doing)something劝告，说服某人做(或不做)某事，通过争论使某人做(或不做)某事3. argue something away(或off)找理由把某事辩解过去4. argue with(或against)someone about(或on) something与某人辩论某事
quarrel ['kw?:r?l]
vi. 吵架；争论；挑剔
n. 吵架；反目；怨言；争吵的原因；方头凿
n.
1. 争吵，吵架，口角2. 不和，不睦3. 争吵原因
vi.
1. 争吵；不和：例句: This newly wedded couple are always quarreling.
这对新婚夫妇总是吵架。2. 挑剔；埋怨：例句: Don't quarrel with your fate. You should take it into your own hands.
不要埋怨命运，你应该掌握自己的命运。
近义词:
wrangle . altercation . squabble . spat .
反义词:
agreement . harmony .
短语
1. espouse someone's quarrel帮助某人争吵；为某人鸣不平；为某人报仇2. fasten a quarrel upon (或 on) someone向某人找茬儿吵架，向某人寻衅3. fight someone's quarrel (for him)为某人鸣不平；帮助某人争辩(为了主持公道或帮助某人取得赔偿等)；帮某人报仇4. find quarrel in a straw找茬儿，挑剔，吹毛求疵5. have no quarrel against (或 with)对…无所责难；没有理由抱怨6. in a good quarrel争吵得有理，有正当争吵的理由7. patch (或 make)up a quarrel暂修旧好，暂时和解，暂停争吵8. pick(或 seek) a quarrel with someone借故寻衅，向某人挑衅；故意和某人争吵9. quarrel of long standing世仇；宿仇10. take up a quarrel
a. 参加争吵
b. 排解，调停 [莎士比亚语]