Instructions
1) Sign in to Outlook on the web.
NOTE: This cannot be done in the Outlook application, or it will reappear a moment after trying to delete it. You will have to sign in to Outlook on the web to follow these steps.
2) Click the settings icon in the top right corner of your browser.
3) Click View all Outlook settings.
4) Click Calendar.
5) Click View.
6) Under "Birthday calendar," uncheck the box next to "Turn on the birthday calendar."
7) Click Save.
Outcome
You have removed the "Birthdays" calendar in Outlook.