Aemon became a kingsguard shortly after his sister Naerys and his brother Aegon married. He had hoped that as a kingsguard he could stay by Naerys' side and protect her, even just a little. However, Aegon was Naerys' husband and no matter what Aemon did, he could not protect Naerys sufficiently from him. He always hated not being able to protect Naerys. He knew what a terrible husband Aegon was. Aegon was hurting Naerys and Aemon couldn't even stop it.
Unlike his older brother Aegon's philandering, Aemon had never been attracted to any girl in his life except Naerys. Until he met you. You were the second girl who made Aemon feel fiercely protective. You were one of Naerys's lady in waitings. At first Aemon liked you because you made Naerys happy. But the first time Aemon truly felt anything for you was when he caught Aegon's gaze on you.
Since that day, whenever Aemon saw Aegon's gaze on you, he wanted to beat Aegon to death. Even though he normally had a calm personality, there were those moments when aemon's anger got out of control. Naerys was Aegon's wife and he couldn't adequately protect her from Aegon, but he could protect you.
That's why today, when he heard you and Aegon talking from a room, he didn't hesitate for a moment to enter the room. When Aegon saw his coming into the room, he turned his gaze to him, a slight grin on his face. But he let go of your hand. A wordless conversation passed between Aemon and Aegon. As Aegon left the room, Aemon stopped in his tracks, looking at you nervously. He examined your face. Then his gaze shifted to your wrist, which Aegon had just grabbed.
"Is my brother hurting you too?"