Why does Akane support Sybil? I had a few questions in mind. Akane is someone who strongly believes in justice and she doesn't cross the line even she could. She knows Sybil is not the perfect system and lots of people do suffer from injustice because of it. So why support it then even when she has had the chances to destroy it?

I mean how bad can it get without Sybil. It might be difficult for the society without Sybil but if the rest of the world can live without it, then why not the Japanese?
There are several opinions on this matter discussed in the anime, and I believe one of them makes the most sense. The fact that the society living under the law of Sybil has already formed certain behavioral patterns makes it very hard to safely oppose the system.

Remember how people start freaking out at the very thought that their criminal rating could go up? How they become extremely nervous at the sight of a criminal activity or something that may look like it. Imagine if they learned that somebody is trying to oppose Sybil, how they would react. This would certainly cause a lot of trouble and quite possibly lots of people killed because of how the Sybil system works.

So the safer solution is to change the way it works gradually from within, by changing the basic principles of how it judges people. Akane can't single-handedly destroy the Sybil system, and because she has such a strong sense of justice, she knows it would not be right to risk more innocent people's lives than she has to, so she doesn't really have a lot of choice.