You don't see justification for the dissent because there really is none. It's pretty cut and dry that requiring permission to exercise a constitutionally protected right is wrong.What I find most interesting about the dissent is the lack of actual legal justification for their dissent. It reads like "Guns are bad and dangerous. We should let Gov regulate them. Oh, and the majority didn't take enough time/effort to understand those two points." There's very little actual reference to any precedent that could justify a contrary ruling.
But did you expect anything less from the liberal justices? They were appointed to rule based on political positions of the left, not on the actual law. They do their job extrodinarily well, the actual law be damned.