Why do we define the Milky Way's rotation in a left-hand coordinate system? When we talk about Milky Way kinematics, we define it as rotating clockwise from top.  In the rest of physics, rotating objects are defined as rotating counterclockwise from top (following the right-hand rule).  Why do we do the opposite when talking about the Milky Way?
The problem, as far as I can tell, is that the North and South Galactic Poles were defined well before we had any idea of which way the Galaxy rotated. It turned out that the Galaxy's angular momentum vector (in the standard right-hand sense) actually points in the same direction as the previously defined South Galactic Pole. Since there's a separate convention for having "north" point "up", you end up with the backwards rotation definition.

William Herschel seems to have started this back in the late 18th Century; I assume his idea was that whichever Galactic pole was in the North Celestial Hemisphere should be called the "northern" pole. (No one back then had any clear sense that the Galaxy necessarily rotated at all.) By the time the actual direction of Galactic rotation was figured out in the 20th Century, the traditional orientation was too well entrenched to be worth upending.