Software bugs in practice are rarely caused by fundamental problems. Sloppiness, incompetence and, in this case, different priorities are much more likely. Removing data is not a priority for Facebook.

People like to invoke all those theorems from computer science. That gives them an air of being knowledgeable. But at the end of the day, it's much more common that the program malfunctions not because of the halting problem, but because the language it was written in doesn't do bounds-checking on arrays, someone made an off-by-one error, or someone copy-pasted some code and the objective of the system was data collection, not data deletion, so the task of reviewing and testing the code was deprioritized in favour of something more profitable.

But talking about how you struggle daily with the fundamental problems of the universe sounds so much cooler.