I see now. Someone else mentioned it too, it’s similar to how we don’t negotiate with terrorists imo.
Personally I’m against all book burning, religious or no. In this instance though, it’s not just that Islamists are against it, as much as it giving them free recruitment ammunition, to help motivate their populace.
There’s always a certain percentage of crazies in any society. They benefit if they can recruit more moderate people to that extremist position. When we attack them, either physically or ideologically, we feed into that mechanism that strengthens them by giving them more of what they want. They say they don’t want us to burn their quoran, but I suspect their leaders are actually extremely happy when we do.