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The twenty-first century marks the dawn of an era of genomic medicine, which holds the promise of personalized medicine with the potential to transform the medical paradigm and offer tailor-made care in the future, in terms of diagnosis, prognosis, and treatment. Today, the sequencing of an individual’s entire DNA no longer poses technological or economic problems, and its purpose is becoming a societal issue that requires ethical reflection among the wider public. Here we aim to discuss the emergence of new practices in genetics concerning so-called secondary data from genome or exome analyses. As an example, access to these data could be given to a family whose child exhibits neurodevelopmental disorders. These data could then reveal the existence of a genetic predisposition to heart or oncological illness within the family, for which preventive or curative treatment could possibly be offered. These practices are already established in the United States, but are still being debated in Europe. In this paper, we seek to ask how the results of secondary data can be interpreted subjectively by the consultant and families and whether they genuinely offer patients and their relatives the necessary conditions for a more open or, conversely, more difficult future to endure. This prompts us to demarcate the notion of an inevitable predestination from that of destiny, which, conversely, can always be created in an open temporality that is subject to the irreducible contingency of the future.