Why does Batmobile in the Dark Knight trilogy have a missile shooting feature? Batman believes in no use of guns, is the rule exceptional for the batmobile?
Combination of things here. First, as @DustinDavis mentions above, this wasn't "designed" for Batman and the capabilities were already on the vehicle. Despite the fact he modifies each vehicle from its military design, Batman probably saw use for the feature and kept it.
Going off of that, Batman does not use the missile feature on people, he instead uses it to break through buildings/walls/etc. so that he can get to where he needs to be.
The capability is also featured in The Dark Knight Rises, as seen towards the end when he uses the missile feature to punch a hole through a building essentially so he can fly the bomb outside the city limits.
Simply, Batman's a crafty guy and uses the missiles for practical, not violent purposes.