Because using it as a "tea" instead of dry matter makes it instantly absorbed into the soils and bound to nutrients there to make it more readily available for plant usage. It isn't lying on the top of the soil like fresh manure would be, waiting to be splashed up onto vegetables with each rain.
People out here in the backwoods have been using pig manure tea on gardens for more years than any of us have been alive, with excellent results, I might add. No illnesses or deaths, either. What city folks do when they move to some acreage and have organic farms, using their VAST knowledge of farming practices
is a great deal different than tried and true methods passed down from generation to generation.
The difference between manures from omnivores vs. herbivores is usually that the omnivore manure has elements that have not been digested fully as they lack multiple stomachs for fermentation and conversion of proteins and some sugars, whereas herbivores have either multiple stomachs(ruminants) or specialized bowels(horses and rabbits) that aid in this break down of nutrients. That is why one is considered a "hot" manure and the other a "cold" manure...it's just one manure is still composting and creating heat, ammonia, etc. and the other is pre-composted by the animal. By taking hot manures and making a liquid from their feces, one captures the nitrogen and other components that enrich the soil without also using the undigested dry matter that is in the actual bulk feces...that matter that is composting hotly if placed fresh on a garden. The tea is powerful stuff and most folks dilute it before side dressing with it.
The point of all that is this...it doesn't lie on the surface of the soil in its raw state, being splashed up onto edibles with every rainfall, creating pathogen problems for the consumer. It is absorbed into the soils and is washed even deeper by the rains, particularly in good, loamy soils found in most established garden plots.