Well, Kaname isn't actually genuinely Yuuki's brother. He was the Kuran family's ancestor. Rido sacrificed his siblings' son (who had been named Kaname to honour the ancestor) as a way to bring Kaname out of a deep, coma-like sleep. The baby's blood wasn't enough for Kaname after centuries without blood, so he reverted back to an infant state to prevent himself from attacking his descendants for their blood. Haruka and Juuri then basically adopted him.
In that quote, Kaname is just saying that he wished he had been Yuuki's real brother, because it would have been that much easier and simpler, and his many-greats-grandson wouldn't have had to die.
Kaname says that because he loves Yuki now, But only if he had been born her real brother he could have had mais true feelings and he just had such a sad past he wish he could've done mais for Yuki and that is why he "babies" her. He says that also because he was actually born again. Meaning that Ride had brought Kaname back to life. So Kaname is really Yuki's ancestor.