I think there's some confusion here about the concept of "identification".

A date of birth is generally considered identifying information because it can be used to implicate other information about your real-life self, and it can have real-life consequences for you if it is known. It discrimantes and differentiates you from other individuals in ways that have real-life implications.

What does a password identify about you? Well it verifies that you are "the same person who set the password on the OS".

So to compare and contrast, A DOB identifies you as...

• a person who may not be allowed to install certain programs or access certain information/content, based on age
• a person in a demographic who may be amenable to certain advertisements
• (if your system is compromised/leaked and age retrieved) someone who may be desireable by predators
• (in the context of investigation or stalking) someone who is not a specific other individual (ie it narrows you down from a pool of individuals)

Having entered a password identifies you as...

• the same person who set up the OS
• ??? - feel free to let me know if you've got anything here.

To consider the act of entering a password as an "identity" is pretty bizarre, and frankly the notion seems contrived just to be argumentative.