Perhaps in the context of a marriage or friendship this argument would make some sense. But in the context of therapy it does not.

First of all, it doesn't sound like LT is giving an ultimatum even though she's perfectly within her rights as a client to do so. If were he my therapist I would have given him an ultimatum a long time ago...."get some training on attachment or I'm finding a new therapist."

Second, you accuse LT of not being willing to examine her feelings, yet the entire issue here is that her therapist REFUSES to help her examine these particular feelings because they are too hard or triggering for him to hear. How on earth is she supposed to navigate that? She hired him to help her, yet he puts up boundaries around her even being able to utter the harmless words that express her feelings.

To hear her say these words (I love you), to help her explore what's behind them (most likely complex feelings mixed with deep roots of attachment pain), and to hold space for her within the context of therapy is literally HIS JOB!