The details are quite murky. However, some believe that in ancient seafaring cultures, there were rare instances where a person who had a strange encounter with the sea or what they thought were sirens, and then faced misfortune. This misfortune was then associated with the sirens in a more extreme way, like a blood curse. It could also be related to the idea that sirens were thought to be able to control the fates of those who crossed their path, and the blood curse was a way to explain the extreme consequences of that interaction.
Since there's no definitive account, we can only speculate. It might have originated from the need to explain natural disasters at sea. When ships sank or sailors disappeared, people in those times, lacking scientific knowledge, might have blamed it on sirens. The blood curse aspect could be an extension of the idea that sirens had a powerful and malevolent influence. For example, if a sailor went mad after a supposed siren encounter, it could be seen as a sign of a blood - related curse, perhaps thinking that the siren's blood had some sort of corrupting power that was transferred to the sailor.