Why is my light connected between two red wires on a circuit with two switches?
It looks like a standard "power on the end, lamp in the middle" 3-way arrangement.  However (for whatever reason) they chose to make the travelers black and white on both segments.   

Travelers can be quite a dog's breakfast, I've seen 3-way circuits where the travelers change colors on every segment.  Choosing the same colors thru makes some sense -- however white should not be one of the chosen colors.  though the far, far better way is to pick a colored tape color such as yellow, and mark both travelers yellow (they are interchangeable, they can be the same color).   

That's because white is special in Code rules.  Colored wires (hots) cannot be remarked to be neutral.  But white wires can be remarked to be a hot wire. The last guy should've made red and black the travelers and tagged white with colored tape in the segment where it served as switched-hot.  That would've been reasonable.