So, I was trying to batch convert a bunch of layers from decimal degree to UTM (I also tried individually with the same problem).
For some reason, there is nothing in the "Projected Coordinate System" folder. Is this because there is some reason this conversion can't be made?
As a note: when I right-click on "Layers" and go to >> properties >> data frame >> coordinate system, I am able to find and assign UTM THERE ... but it just doesn't seem to want to let me change the individual features.
(I've attached a screen shot)