When you flush the toilet without closing the toilet seat lid the bacteria that is in the toilet sprays into the air as tiny water droplets even though you may not feel the water or see the water going through the air.
So at public toilets that don't have a lid to cover the toilet seat when you flush all that bacteria from the toilet and peoples feces fly into the air and infect other things around it.
At home I always flush the toilet with the toilet seat lit closed fully to prevent spread of bacteria.