Where did the practice of "right foot first" come from?

by ScriptorOfScripter

In Islam, there are a bunch of rules about putting your right foot forward first, with the exception of bathrooms where you should step in with your left foot. But I know this idea didn't start there.

The Romans referred to the left as "sin" like "sinister" (at least for marching orders), but they're not the oldest either. As far as I can tell, they got that idea from the Greeks who would start their battles by stepping with their right foot first for good luck. I know the Greeks practiced this as far back as the reign of Philip II of Macedon. That brings me to my question.

Where did the Greeks get this practice from, assuming they didn't start it? Where is the origin? Thanks!

SalvationInDreams

Follow-up:

In more modern times this is less common - drum and bugle corps, for example, which are descended from a military marching tradition, generally step off left. This follows across high school bands, military school bands (notably Navy), and other college groups. A major exception is Cadets, who step right, and I believe Glassmen may as well. The reasons I see for it vary but none are related to ancient thoughts about the left side.

Whatever the reason, stepping left is quite common today. Assuming the OP’s examples are correct, what led to that practice changing?