I had the same issue. Using my phone, this is what I did.
1. Open Facebook using Safari in the desktop version, not in the app.
2. Tapped EVENTS
3. Bottom right of page, right above the language selection box is a box where it says "You can add your events to ... calendar. Once you add them, they will stay updated. Learn More. Upcoming Events. Birthdays"
4. Tap "Upcoming Events" and my iphone brought up a permission box to subscribe. Grant permission.
5. Tap "Birthdays" and grant permission.
How do I export my events or friends' birthdays? | Facebook Help Center | Facebook
How do I export my events or friends' birthdays? You can export events and friends' birthdays from Facebook into calendar programs like Apple iCal, Microsoft Outlook and Google Calendar.
To export all upcoming events or birthdays at once:
- Click Events on the left side of your homepage.
- On the bottom right side, below Find Events, click Upcoming Events to export all upcoming events. Click Birthdays to export all upcoming birthdays.
To export an individual upcoming event:
- Go to the event you'd like to export and click > Export Event.
- Select whether to save the event to your computer or send it in an email.
- Click Export.