I think this is very elegantly put, in a way that is clear and simple and rings very true with me. I think it is a common smart-person trap to try to change others, meaning that smart people can be more confident of the their correctness and perhaps actually are more correct, in the abstract sense of how to problem solve or go about doing something. My advice to the OP would be to ask yourself whether you sometimes have conflicts outside therapy with people, especially a partner or significant other, about who's right about the best way to go about doing whatever.

The desire to control people is a complex one, and only partially fueled by a perception (correct or not) that one is better at figuring things out than other people. My H, who was a very intelligent man, had the problem solving skills of someone far less intellectually gifted, so in my experience, intellect and the ability to think through something and how to approach it are different. He would make some really dumb choices in response to conflicts at work. And I was always trying to tell him what to do and how to approach it, until I learned that my main point was to control what he did, and it really wasn't my business how he handled his business. I'll put aside the dealing with conflicts that were part of our marriage or family, as it's not so particularly relevant here.

I think anytime therapy moves into the therapy where the client is trying to change the therapist, change the way the therapist sees something, even if it's about the client, or change the way the therapist handles the therapy (outside reasonable discussions that are part of any collaboration or asking for what the client needs), or otherwise how the therapist does their business, it's likely to doom the therapy, especially with a wishy-washy therapist (as opposed to someone who is flexible in how they work with clients) or a therapist that just caters to whatever the client wants. I would never pay money to try to change the therapist, or the therapist's ideas, even about me or about how s/he perceived something that happened in therapy.

It is a pretty basic principle that two people in the same room often do not see, hear, or experience the interaction the same. When I was in Psych 100, the prof had a stranger come into the classroom and they argued briefly, and then the stranger took the prof's pen and fled. At the time the students were unaware this was a demonstration, and this was before students had laptop computers, phones, or other recording devices. The prof asked us to describe the incident, and it was eye opening in not only the basics of the "attacker" description (relevant in legal eyewitness testimony, which can be terrible), but what they argued about (some thought they were lovers and arguing about their relationship; others colleagues or even strangers I think); the stranger stole the prof's purse, chalkboard erase, etc, it went on and on.

I think what goes along with trying to give up controlling other people is a healthy skepticism about your own "truth" as it relates to other people. It is good to have a solid core understanding about yourself and your experiences, but when those experiences involve other people saying and doing things in interaction with you, I try to remember that there is room in my understanding for the other person's perception. Therapy has been a safe place for me to question this, to ask my T about whether he was angry at me, or whatever, in prior sessions. His perception is often different or he's not as tuned into what happened as I am, if I've been stewing about it for a week or longer. He never gaslights me (which is a deliberate attempt to change my perception or make me doubt my perceptions, not just a disagreement about what happened) and I can usually understand how his perception and mine connect in some way, or can see how he perceived something as real even though I originally saw it differently.

So in my experience, checking out my perception of other people in relation to me has been a good experience and kept me humble in the sense that I used to think I was good at "reading" people, but it often turns out I'm good at thinking I read people. I go back to that psych 100 experiment often in remembrance of how very little about interactions and my beliefs about other people are some sort of objective truth.

When I started giving up my desire to control people and my belief that I had some superior ability to discern the truth about others, my relationships became deeper, more connected, and had an ease I hadn't experienced before. Especially my marriage. I think giving these things up gives others more room to be themselves in a relationship with me, it makes them feel safer to tell me how they see things, and they accept our differences more readily.

I don't know if any of this long-winded explanation applies to what is going on with you and your T, but I think perhaps trying to check out your perceptions of her and her abilities with her might be more fruitful than making assumptions and conclusions without her as part of the conversation.