Why does songbird care if president myers dies?

Ive read if you fail to save myers in time she gets pissed but doesnt she betray myers and she doesnt even like her does she? Im just wondering why she would be pissed? Its been a bit since playing it but i dont think i ever got the impression that songbird actually cared much about myers if at all except for when she asks V to save her. Is there a reason she geta pissed or is the idea thst if you fail to save myers since you dont yet know about any of the details of songbirds betrayal.. something like that that?