The reason is it falls under the same law - cars, bikes, forklifts, tractors, etc. Basically: alcohol == walk. The curious thing is, you lose your driver's license for bike DUI. If not for an accident, people get canned usually for recidivism, first senteces are suspended. I've been stopped for a breathalyzer once, in the middle of the night, on an empty bike path in Warsaw.
Well, Belgium, heh, we are a bit different when it comes to bike infrastructure and roads in general. A lot of traffic goes through local roads, small towns and villages often lack means of transport in the evening, and people drink a lot - figure out the rest. A drunk biker can be a danger to himself and the drivers, but there are enough laws to punish somebody for behaving dangerously on the road, no need to get nazi on everybody who's been for a few in a pub. Well, it's ridiculous.