It can potentially, but not as... "easily" as some rumors/tales could suggest. Unless you are a small child or very frail, if such an attack were to somehow break your arm, it would probably injure the swan much worse, which would be a poor trade off for it. So it would have to be in a really aggressive mood, to forgo its sense of self preservation, and other variables would have to line up... like I don't know the odds? People can break their arms just by falling over though, its not really a common issue though.
As for where the idea/myth came from? Probably their occasional aggressive, territorial, protectiveness. Probably in relation to how calm, and serene, and elegant they might otherwise seem. So such tales probably get perpetuated as a cautionary tale, to be weary of certain swan behavior, like if they are protecting its nest, a partner or its baaaabbbbiiiesss!
Magpies are similar. In Australia, some can kill you! Except, usually those deaths are rare and the result of people be attacked by a magpie and cycling into cars etc they have a bad reputation, and can be aggressive and annoying, but not really deadly.
Source: I use to train Swans for Hollywood movies, for 4 decades. I was what they call a Swan Whisperer. I know everything there is to know about creating and maintaining a swan army.
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