This is behavior that occurs naturally and will eventually rectify itself with the cygnets leaving the area or at least the immediate area of the parent swans' nesting habitat.

Once the young swans turn completely white, which occurs at approximately 9-12 months of age, the parents start chasing them from the area because they are preparing for the next nesting season. The parents also know that they have taught the cygnets everything they need to know to go out and find themselves a mate and permanent nesting/living/breeding habitat.

The young swans however, are completely perplexed about how one day the parents are protecting them and the next are turning against them and wanting them to leave their parents.

Think of this time as in human lives when a child (teenager) no longer wants to be around the parents because they think that they are old enough to make decisions and go out on their own. Then, when it is time to go out on their own (college), suddenly the parents no longer want the child to leave. In the wild, this behavior is reversed. The cygnets do not want to leave the fold and the parents can't wait to get rid of them to start another brood.

Again, this behavior will eventually work its way out and the cygnets will stay away from the parents and their area of the habitat. And, eventually, the cygnets may completely leave the area to find another habitat.

Now, having said this, we have seen where cygnets go out, form a bond with another swan, have cygnets and still return back to their parent's habitat (if tolerated by the parents outside of the nesting season) because there is no other suitable habitat in the area for continued resources such as shelter from inclement weather, predators and the habitat offers high food resources that is ample to accommodate a large number of swans and other waterfowl. The Regal Swan