System Fields cannot be deleted because they affect other areas of the system.
Date of Birth
What can I do instead?
If the Field you were trying to delete is a System Field and therefore cannot be deleted, and it's currently set to be visible on the Customer Profile page and/or included in Forms, you can either:
Edit the Field from Settings >> Customer Fields so that it's neither shown on the Customer Profile page or Form(s).
Remove the Field from the relevant Form(s) from Forms/Documents >> Customer Forms page.