At this point I can only come to one of two possible conclusions (1) the show, like most media, has no idea how to write complex, interesting, complete female characters or (2) Liz's emotional merry-go-round with Red is completely intentional and a needed preface to further actions.

Evidence for the first idea comes from, well, a lack of diversity and representation of women in pretty much all of television/movies. Even Sorkin, possibly my favorite film/television writer, has notorious difficulty depicting female characters that can compete with their rich, complex male counterparts. It is an industry wide problem. One of the reasons why I love House of Cards is the amazing female characters who have their own desires, motivations, and personalities that aren't driven by male characters. This type of independence may not be possible here, given Red's practical omniscience, but female characters like Madeline Pratt who can compete in a battle of wits with Red would be most welcome. Heck, Samar has been great because she has a backstory, her own set of skills, and her own motivations.

Evidence for the second possibility is sprinkled throughout the show in a way that stresses Liz's volatility. Red verbally mentioned this trait to Sam, she has the "warrior gene", and she's shown violent tendencies from the beginning when she stabbed Red in the neck with a pen. As Red's protection grows more controlling, and all her moorings to a normal life are released, increased volatility is a natural response. Combine a volatile nature with repeated concussions/blast injuries in a high stress environment and you get the emotional merry-go-round of "You are awesome... Now I can't trust you." In the end she could kill Red and it wouldn't be out of character. Granted, I wish she was a richer character on the journey to that end, but her actions would make sense in context.