Remembering birthdays is a reflection of how much someone cares about birthdays. There’s no need to read anything more into that.

Many people (this thread is an example) are either completely indifferent to birthdays or even dislike them. To us (I’m indifferent) birthdays are totally pointless and basically a fact related to identification, like a student number or social insurance number. I remember my student and social insurance number because I have to, in order to function at school and in society. I don’t ask anyone else’s student numbers because it’s entirely pointless and useless information to me.