information about a person

Not only one person, but also their relatives, who didn't consent to begin with. You of course don't get all of it, but if you e.g. have the DNA of a parent, then you also get information about their children.

Say for example they have some genetic predisposition for an illness, then their child is probably also more likely to get it. Better hope that in the future there are still laws against using this kind of data for determining health insurance.