Originally Posted by
nesdog
.... noticed that there was an arrow indicating tire rotation direction on it. Naturally, I mounted the tire backwards, based on this! ........does it matter?
Yes and
No
it depends on the tire and purpose. On most road tires, tread has little effect so direction hardly matters, if at all. That's especially on smooth road tires with groves or "stippling" cut in. These have zero meaningful effect, so it really doesn't matter.
OTOH, mtn tires with aggressive knobby treads are often very directional. Some that are made specifically as rear tires for use in mud or sand have knobs shaped like scoops and will really lose pushing power if run backward.
So look at your tires, decide where and how you ride, and draw your own conclusions.
Now that you think you have it, here's another wrinkle. If using the same directional tire on both wheels, you might want to run the front backward. That's because you want best grip under power on the rear wheel, but on the front you want that same grip when braking.