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So I was watching some random FMA stuff on youtube, and my mom was behind me and she asked why Al was wearing an apron. Does anybody really know, or is it just kind of always there for no reason?

A few of the omake in the manga series makes fun of this. There probably is no real reason, but if you look closely, you can see black where the groin would be (just as you see black in that headshot there). That means empty space or space that could reveal the body that would be there. Perhaps it's there to cover up the emptiness inside the armor.

However, that's been there when Ed put Al's soul in the armor. So it could just be the design and style of the armor.