This behavior may be explained in two ways. Either both swans are males or females and there is a territorial issue of who owns the lake and all of its resources, i.e., food, etc. There is a hiearchy in swans just like in any other animal or bird species and one of these swans is playing the dominant role.

The second issue may be that because we are now entering mating season, the sex hormones are kicking in and territorialism is also coming into focus. Continue trying to feed the swans as you currently are doing and see if the behavior improves within the next month (mating behavior and sex hormones may settle down). If not, no matter what type of intervention you pose, the swans will need to work this out themselves. The Regal Swan