Reminds me of the interesting number paradox[1]. This can be easily extended to dates too in this manner:
Every date is interesting. Proof by contradiction: If there exists a non-empty set of uninteresting dates, there would be an earliest date in this set. But the earliest such date is itself interesting because it is the earliest uninteresting date, thus producing a contradiction.
Every date is interesting. Proof by contradiction: If there exists a non-empty set of uninteresting dates, there would be an earliest date in this set. But the earliest such date is itself interesting because it is the earliest uninteresting date, thus producing a contradiction.
[1]: https://en.wikipedia.org/wiki/Interesting_number_paradox