Why did Akito abuse Yuki?

I think you've got this wrong do you mean why is Akito so protective over Yuki? If that's what you mean it is because traditionally the rat was the favorite because he arrived at the feast first. Akito is very protective over Yuki because he could as Yuki's parents basically gave Yuki to Akito to gain his favour and so Akito pretty much owned Yuki while he was younger and used this power to make his life misserable.