Forgetting birthdays is a system problem, not a memory one
Almost nobody forgets a birthday because they do not care. They forget because they were relying on memory, and memory is the wrong tool for dates that arrive once a year with no warning. Feeling guilty about it does not help; building a small system that does the remembering for you does.
The fix has two parts, and most people only do the first. Capturing the dates is the easy half. The half that actually matters is lead time: being reminded early enough to do something. A reminder that pops up on the morning of the birthday has technically worked and practically failed, because there is no time left to plan a gift, book anything, or write more than a rushed message.