Why do we wear costumes on Purim?

Actually, the title of this post is wrong. I don't mean to explain the reason for Purim costumes, but to hazard a few guesses as to how the custom was established. Here they are

• At a particular moment in time, a group of illustrious Rabbis gathered to formally address our spiritual shortcomings by establishing new customs. This is how we got upshurin. Its also how we got Purim costumes. (My view: BWAHAHAHAH.)
• At a particular moment in time, perfectly good Jews came up with a perfectly good Torah  reason for wearing costumes. So they started doing it (likely after asking a shaylah) When the Rabbis acquiesced the custom caught on. (My view: Meh.)
• At a particular moment in time, Jews had Catholic neighbors who wore costumes in celebration of Mardi Gras. So the Jews copied it - just as we copied Upshurin from Muslims, just as we copied clothing styles from Polish noblemen, just as we copied leaning at a banquet from Greeks, and just as we copied the idea of using lights as decorations in our sukka from Christmas trees. (My view: Who know if this is really what happened, but of the three this is the only one supported by anything resembling evidence. The very first mention of costumes  for Purim is from a 15th century Italian teshuva. Its author and his audience would certainly have seen Mardi Gras costumes.) 

And why do the Catholics dress up for Mardi Gras? Unclear. The celebrations themselves have been linked to Lupercalia a February Roman festival with circus elements  that scholars believe the church co-oped.

Search for more information about Mardi Gras at4torah.com