The only reason I can find online seems to suggest that it is just because AHA said so. I seem to remember reading somewhere once that it was related to finally repealing parts of Prohibition that allowed for beer making by individuals at home, but I can't find anything about that. Anyone have any other historical references or reasons?
As a member of the AHA Governing Committee, the reason I know of is that it just is. From the AHA website...
On 1988, May 7 was announced before Congress as National Homebrew Day. The American Homebrewers Association (AHA) created AHA Big Brew as an annual event to celebrate National Homebrew Day around the world. AHA Big Brew is held each year on the first Saturday in May.