Cat’s real problem is that’s she’s given Kara (why not Linda, writers?) no reason to trust her (not part of Clark’s inner circle, abuses the staff, sees Supergirl as a scoop). The writers’/studio’s/network’s problem is that they’ve given the viewer no reason to apply “The fewer who know [superhero’s identity], the fewer who get hurt.” CBS may be at fault, too: likely angry at Warner Brothers for letting Person of Interest’s writers run that show into the ground and rely on crazed fans to silence the network, probably wanted to go to superhero-comics cliches as a means of making the show “better,” and to avoid PoI’s descent from sci-fi cop drama to nihilistic trash (IMHO; mo on that later).
Kara, meanwhile, is scared of her boss anyway, and essentially works two high-tension jobs already, and so probably is incapable of conceiving of Cat as anything but a weight.
Or the whole thing is misapplying our reality’s version of human nature to the show’s version of sapient nature: real-world human interactions and relationships may not apply to a world of high-powered people/weapons/equipment/events at every turn. But who’s misapplying what to which, dear reader?