Digital BW, The Print

I have wondered this question for years, and have never asked it:

If you start with a big scan for print, say, 20"x20" at about 240dpi, 
and then you wanna rez that down for display on the web, say 
about 600pix by 600pix at 72dpi, and you do, in one fell swoop, 
the image becomes very fuzzy. If you USM it at about 75 or 100%, 
it helps, but still doesn't look great.

Does anyone know why it gets fuzzy? And does anyone know a 
great technique to preserve sharpness and detail when 
prepping for the web, from an archive scan?

Thanks. Mark Tucker