Why are U.S. coins printed with the obverse facing upside-down relative to the reverse?

No one knows! The US Mint just goes with the flow...(this process is by the way called Coinage Orientation)

Why is the Flip Side 'Flipped'? In other words, why, when you flip a coin over after looking at the heads side, is the picture on the tails side upside down?
All U.S. coinage is produced with what is commonly called a "coin turn." That means that the reverse side (tails) of the coins is upside down to the obverse side (heads). While we have researched the history of this practice, we have been unable to determine the exact reason for this custom. The Mint still produces U.S. coinage in this manner for traditional reasons and not due to any legal requirement.

Source: Page on Usmint