Refer to this preceding sentence,"We don’t talk, we hold forth. We don’t converse, we expound...."
I'm pretty sure the author is trying to conjure up a mental image of the way hatpins were used as self-defense weapons. The "expounding" is a way of hiding by being on the offensive. It's really not different to the way social media works today. The insecure person just can't leave a point alone, they have to "win" every argument, even when nobody else wanted to have that argument, by showing off their opinion and why they're absolutely right (even when they're not). Google for pictures of hatpins if you've never seen one and the imagery will make sense. He could just as well have said something like, "I can't stop hammering my point across," which is another metaphor using a similar physical action.