Why does Bane want to destroy Gotham city?

"Doesn't matter who we are, what matters is our plan".

We find that the plan is to destroy Gotham, it doesn't matter who is carrying this out, whoever they are, they are upholding and executing a plan. Well, in order to see the plan in its purest form, we have to ask "Whose plan was it originally, it doesn't matter who is pursuing it now, but what was the original plan?"

To answer this, we have to go all the way back to Batman Begins, it is Ra's Al Gul's plan. So the question isn't really "Why does Bane want to destroy Gotham?" but "Why does Ra's Al Gul want to destroy Gotham?" He explains in the League of Shadows' Temple while training Bruce (albeit, Ducard rather than Ra's). He says that Gotham is the epitome of corruption and injustice and has to be taken out to restore balance and justice.

Now, sure, Bane and Thalia have their own reasons for wanting to uphold this plan. Talia wants to simultaneously punish her father's murderer and accomplish his incomplete work. Bane wants to support Thalia as he sees her as purity and redemption, he maybe even has romantic feelings toward her (which is more literarily ambiguous than commonly thought).

BUT THE WHY IS TRACED ALL THE WAY BEYOND BANE AND TALIA!

Think of that theory and reconsider the line "it doesn't matter who we are, what matters is our plan"