He just wants somebody like Lyra who won't judge him, who will sit by and listen. But, Akito recalled Setsura's recent break down. 'After seeing her like that, He is reassessing his interactions with her.' At the beginning he had no idea. Even though he saw how vulnerable she was after those nightmares. Akito didn't think there was a deep rooted fear and anxiety in the girls heart.
He does not want to burden her anymore.
It's not like he doesn't understand where Lyra is coming from. Talking about this with Setsura would be better, since she will understand. However, "I don't want to burden her too much. I'm being hypocritical since I told her not too long ago to rely on me. But..."
Lyra sighed, "I've always felt that you dislike yourself Akito."
"..."
"Even back when she was here, you didn't look truly happy. However, with Setsura I feel it's different."
Akito's eyes widened at Lyra's words.
