Abdul Rahman opposed Muawiya's appointment of his son Yazid as successor to the caliphate. When Marwan ibn al-Hakam announced this news to the people of Madina, he tried to give it legitimacy by saying that it is the way/custom (Sunnah) of Abu Bakr and Umar. Abdul Rahman objected to this reasoning, saying it is the customs of the Byzantines and the Persians, not the custom of Abu Bakr not Umar, and that neither Abu Bakr nor Umar have appointed their own progeny as their successors. Marwan tried to malign Abdul Rahman by quoting Quran 46:17 and falsely claiming that this was revealed against Abdul Rahman himself. Marwan tried to capture Abdul Rahman, but the latter fled to the safety of the house of his sister Aisha. ref
Some sources claim that Muawiya ordered Abdul Rahman to be poisoned for opposing Yazid's succession.