Dear Johannes Kingma,
Good day! Thank you for posting to Microsoft Community.
To remove the Birthday calendar from your Outlook on the web, Kindly sign in to your Outlook on the web and go to calendar -->Select Add Calendar --> Birthdays -->uncheck "Turn on birthday Calendar" checkbox. Then check if the birthday calendar is removed from your outlook. You can refer to the screenshot below.
If the issue still persists, May I please double confirm if you are using a Microsoft 365 business email account or Microsoft personal account such as Outlook.com, hotmail.com or live.com?
I look forward to your update. If you have any other question, please feel free to let me know.
Thank you for your precious time. Have a nice day. Sincerely,Libeamlak | Microsoft Community Moderator