We have seen this same behavior in some swans (not all). It usually is the male who takes the bread and the female hisses. However, we have a female which will take the bread and the male will show us his feathers and start to chase. This behavior usually occurs during mating season and people or other birds/animals may be seen not only as predators but also as rivals. Right now, mating season for mute and black swans are upon us so that may explain why you are seeing this behavior.

It could also be the various personalities of the birds. Some swans are more friendly than others. The Regal Swan