A lot of red flags are going up from this post for me.

First, You are having classic countertransference issues but are not bringing them into the therapy session but rather personalising them. Brush up on countertransference NOW.

Second, the fact is this client probably does this with everyone in her life. Your job as the therapist is to create a therapy session in which you conduct THERAPY not judge her and how she chooses to be in the world but to offer her the chance to gain insight from how she operates into the world and then offer her the tools to change if that is what she chooses to do. This is about her issues, not yours. I would suggest to a more skilled person to use the countertransference as something to discuss in therapy because the therapeutic relationship is a microcosm of how the client operates in the greater world. You could use this as an opportunity to explore and examine how she negotiates relationships and help her understand how her approach of "utility" in relationships makes other people feel about her and how this may be impacting her life.

However you have personalised it and made it about you and until your clear up your countertransference crap the approach I suggested will only come across as unskilled and petty.

Third, I suggest you get supervision right away from a highly skilled therapist/supervisor and work out your skill set around ethically managing countertransference in therapy and commit to making yourself a better therapist.

Finally, Your client is giftwrapping you the material she wants to deal with in therapy and you are blind to it. The fact you say you cannot figure out why you are resentful and have a hard time figuring it out is clear indication of this blindness. You must work on this if you want to grow and succeed as an ethical, compassionate, connected therapist who works with clarity in his/her practice.