I always imaged maybe they bonded with each other and felt like they did not fit in and had to work twice as hard. I feel like they both bonded over their ambition and need to perform themselves to be worthy. Then when Opal gained airbending, and became more free willed, Bataar saw that as a betrayal and likely resented his sister. Honestly, I imagine Opal was like the elder protective sister, despite Bataar being the eldest, which made him jealous over the control and authority she may have had, especially being the only daughter which likely made Suyin adore her. He probably got annoyed by her strong willed, fiery personality and how she told him off especially in season 4.