Dic: a bone of contention

• The main bone of contention is the temperature level of the air-conditioners.
• The examination system has long been a serious bone of contention in this country.
• The main bone of contention between us is our children's education.
• We've fought for so long that we've forgotten what the bone of contention is. 
• The question of a fence between the houses has become quite a bone of contention.

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■ If a particular matter or issue is a bone of contention, it is the subject of a disagreement or argument.

■ something that causes arguments between people.

■ something that people disagree or argue about.

■ Fig. the subject or point of an argument; an unsettled point of disagreement.

... Cobuild, LDOCE, Macmillan, McGraw-Hill Dictionary of American Idioms and Phrasal Verbs.