All information is potentially personally identifiable. For example, perhaps you take data on favorite movies and strip away every bit of PII except sex and bi

All information is potentially personally identifiable. For example, perhaps you take data on favorite movies and strip away every bit of PII except sex and birth year (as you stated). Now let’s say I take the stripped data and target some facebook ads to people of a specific sex and birth year and have the ad be for people who love a certain obscure movie, doubling down on a second obscure movie and so on. Eventually I could have a reasonable chance of determining which other movies a unique individual may like based on the stripped data. Obviously irrelevant for movies, but more relevant for prescription drug uses, sexual preferences etc. The point is that with enough outside data available, even data stripped of PII can be de-anonimized.