Why are my corners "inside-out" in Illustrator?

There are 2 big things I don't get about this image (two identical paths in Illustrator, one of which is reflected, with a pretty simple brush applied to them both in order to highlight the issue)

1. What are these "inside out" corners, and how can I get rid of them? It is nothing to do with the brush because I've seen this happen with very simply shaped paths (i.e. a basic 1-2pt stroke on a triangle) as well.


2. I'm also curious how the exact same shape has a stroke applied in a completely different way. The above shapes are identical except for (obviously) being reflections of one another (this is the above shape deconstructed.

Some notes:

* These are two identical paths (as noted above) with a stroke applied to each simultaneously.

* To make the shape, I merged a circle with a triangle, then adjusted the points manually.

* One is a reflection of the other, so they should be completely (symmetrically) identical.