- Deducing based on my median friends' ages.
- Easily deducing my approximate age from my Linkedin profile.
- Any of the numerous other private people data sources they have access to or have bought over the years. I'm sure my birthday and basic details are in some of those. It's impossible to get those all deleted once the information is out.
- Day and month are easy, because everyone wishes me happy birthday in the messages and wall posts. All that's remaining is the year, which could be easily deduced from Linkedin and other third party data sources. - Which I've mostly cleaned up now, until Facebook exposed it all again.
- I had a profile for a few months in 2005 before deleting it. Used a different computer, different location, different email and everything for this new one a decade later, but probably they've connected the identities. Looks like if you ever tell Facebook some private information, it's non-revokably theirs to expose to the world forever.
Facebook invests very heavily in machine learning / AI, and uses it heavily through out their platform. They collect and buy tons of data both on the site and from third parties. This deduction is trivial for them.
The bad part is not so much that they deduced these details about me though, it's that I specifically made it clear that I didn't want any age public, let alone the real age, and they exposed me anyway.