Well, a couple of the points in this article seem dumb.

Point 1: Cat Grant is a terrible role model. Cat Grant is supposed to be a role model? That's not what I've seen. The extent of role modelyness that I've seen was Kara asking her for advice once in episode two. Besides that, as the author notes, her nature is entirely unrolemodely. We haven't even seen any indication that Kara particularly likes Cat at any point in the show. Kara asking Cat for advice was an indication that she was confused and at her wit's end over her proper life path, to the point where she would seek advice from the last person she would normally go to. If you're really determined to take life lesson from this show, instead of looking for an example of a perfect role model (there's no such thing as a perfect role model in real life), take it as a lesson that there's something to be learned from everyone, even generally shitty ones. Also, don't try take life lessons from TV shows. It's really not a good idea.

Point 2: A strange minirant about secret identities.

No one in the FlArrowverse can keep a secret identity, so why should Supergirl? First of all, the discussion of secret identities was probably for the benefit of viewers who are newer to superhero stuff. Say the extent of their previous familiarity with superheroes was the MCU movies - not entirely unfeasible - they might not be accustomed to the idea of secret identities. Besides that, Flash and Green Arrow do have secret identities. Yes, people joke about everyone knowing their identities, but actually only the people close to them know. Everyone close to Kara (all three-ish of them) know too. And Barry has been encouraged to keep his identity secret as well (Oliver does it naturally because he's a psychopath addicted to secret-keeping).

Side note:

Is anyone else curious as to why the DEO has a closet full of evening wear? Probably for undercover operations.