bone of contention

a bone of contention (between sb) (something to fight over; a reason for quarrels; the subject or point of an argument; an unsettled point of disagreement) — яблоко раздора; предмет спора; предмет препирательств; повод для спора, разногласий

Example 1: The use of the computer was a bone of contention between Lewis and his little sister.— Льюис с сестреркой все никак не могли поделить компьютер. Компьютер был постоянным поводом для споров о том, кому им сейчас пользоваться.

Example 2: The boundary line between the houses has become quite a bone of contention.

Example 3: The best way to roast a turkey remains a bone of contention among even well-seasoned cooks.

Example 4: Vic believes fervently in buying British, and has frequent rows with his eldest son, Raymond, who favours a disposable plastic razor manufactured in France. Not that this is the only bone of contention between them, no, not by a long chalk. The principal constraint on the number of their disagreements is, indeed, the comparative rarity of their encounters, Raymond invariably being asleep when Vic leaves for work and out when he returns home. (Nice work. Lodge, David.)

also
[яблоко раздора]