Without having a concrete answer, I would guess that it is just a standard to keep them all in perfect step. If no matter the branch, all soldiers start on the same foot then there is no confusion on the parade ground.
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The marchers were originally civil rights protesters. This was then hijacked by the IRA and turned in to an armed assault on the soldiers who were on peace keeping duty. The end result was pretty much what one would expect when an amateur army (IRA) tried to take on professional soldiers face to face. Subsequently there have been 3 inquiries. The first two held while memories and witnesses were fresh (and protected) cleared the army. The third held many years later and with no protection left for witnesses blamed them. Subsequent to this photographs have emerged of Martin McGuiness ( a "witness" who blamed the soldiers) proving he was IRA a bombmaker and a weapon supplier to those attacking soldiers -
You should wear the left shoe on your left foot.
Antietam
26000 soldiers
Well this question needs to be more specific as in American Soldiers, British Soliders.. But I assume you mean American Soldiers and there are about 20,000 left. As of November 25, 2011.